PHYSICAL    CHEMISTRY 


PHYSICAL  CHEMISTKY 

ITS   BEARING   ON   BIOLOGY 
AND  MEDICINE 


BY 


JAMES  C.  PHILIP,  M.A.,  PH.D.,  D.Sc. 

ASSISTANT  PROFESSOR  IN  THE  DEPARTMENT  OP  CHEMISTRY,  IMPERIAL 
COLLEGE  OP  SCIENCE  AND  TECHNOLOGY,  LONDON 


SECOND    EDITION 

SECOND  IMPRESSION 


NEW  YORK 

LONGMANS,    GREEN    AND    CO. 

LONDON:   EDWARD   ARNOLD 

1915 


/ 

BIOLOGY 


? 

^l 

LIBRARY 


PRINTED  IN  GREAT  BRITAIN 


PEEFACE 

THE  conceptions  and  methods  of  physical  chemistry  have 
been  extensively  utilised  during  recent  years  in  attacking 
biological  and  physiological  problems,  and  the  results 
which  have  followed  this  application  of  physico-chemical 
principles  are  not  only  of  very  great  interest  in  them- 
selves, but  are  full  of  promise  for  the  future.  Students  of 
"biology  and  medicine,  however,  cannot  truly  appreciate  or 
co-operate  in  this  work  unless  they  are  familiar  with  the 
underlying  principles.  It  is  as  a  sketch  of  the  physico- 
chemical  basis  for  this  modern  treatment  of  biological  and 
physiological  problems  that  I  have  written  the  present 
volume. 

The  book  originated  in  a  course  of  lectures  delivered 
to  biological  students  at  the  University  of  London  in 
1909,  but  since  then  much  fresh  material  has  been  in- 
corporated. I  have  endeavoured  to  give  a  systematic 
exposition  of  physical  chemistry  so  far  as  it  has  a  bearing 
on  the  problems  in  question,  and  to  illustrate  the  applica- 
tion of  physico-chemical  principles  by  examples  taken 
fro~n  the  fields  of  biology,  physiology,  and  medicine.  Since 
the  book  is  intended  chiefly  for  students  of  these  sciences, 
the  use  of  mathematics  has  been  avoided  as  far  as  possible, 
and  the  reader  is  assumed  to  have  only  an  ordinary  ac- 
quaintance with  physics  and  chemistry.  Numerous  refer- 

355186 


vi  PEEFACE 

ences  to  original  papers  are  given  for  the  use  of  those 
who  may  desire  to  follow  up  any  particular  line. 

Of  larger  works  which  have  been  frequently  consulted 
in  the  preparation  of  this  volume,  the  following  may  be 
mentioned  :  Physikalische  Chemie  der  Zelle  wid  der  Gewebe., 
by  R.  Hober;  Physikalische  Chemie  uiid  Medizin,  by 
Koranyi  and  Bichter;  Grrundriss  der  Kolloid-rhemie,  by 
Wo.  Ostwald.  I  desire  to  thank  Professor  Benjamin 
Moore  for  permission  to  reproduce  Fig.  22,  and  Herr 
W.  Engelmann  for  permission  to  reproduce  Figs.  4,  6, 
10,  and  14.  I  must  also  express  my  indebtedness  to 
Professor  Groom,  Dr.  Harden,  and  Dr.  Senter,  who  very 
kindly  read  parts  of  the  MS.  or  proofs,  and  made  many 
valuable  suggestions. 

J.  C.  P. 

LONDON,  June  1910. 


PREFACE   TO   THE   SECOND   EDITION 

THE  chief  new  feature  of  this  edition  is  the  addition  oi 
a  chapter  on  electromotive  force.  The  treatment  oi 
permeability  in  Chapter  V  has  been  extended  by  a  shorl 
account  of  Czapek's  researches  on  the  surface  tension  oi 
the  cell  membrane,  while  references  to  recent  work  have 
been  inserted  throughout. 

J.  C.  P. 

LONDON,  October  1913. 


CONTENTS 


7AP.  PAGE 
I.  GASES  FROM  THE  STANDPOINT  OF  EXPERIMENT  AND 

THEORY.    DIFFUSION  PHENOMENA       ...  1 

II.  ABSORPTION  OF  GASES  BY  LIQUIDS      ....  20 

III.  OSMOTIC  PRESSURE 33 

IV.  THE  COMPARISON  OF  OSMOTIC  PRESSURES.    ISOTONIC 

SOLUTIONS 54 

V.  PERMEABILITY  AND  IMPERMEABILITY  OF  MEMBRANES  75 

VI.  VAPOUR  PRESSURE,  BOILING   POINT   AND    FREEZING 

POINT  OF  SOLUTIONS 86 

VII.  THE  BEHAVIOUR  OF  SALTS,  ACIDS,  AND   BASES   IN 

AQUEOUS  SOLUTION 114 

VIII.  ELECTROLYTIC    DISSOCIATION  ;    PHYSICAL    AND    BIO- 
LOGICAL APPLICATIONS 136 

IX.  COLLOIDAL  SOLUTIONS 177 

X.  THE  SEPARATION  OF  COLLOIDS  FROM  THEIR  SOLUTIONS  201 

XL  ADSORPTION 219 

XII.  CHEMICAL    EQUILIBRIUM    AND    THE    LAW    OF    MASS 

ACTION 244 

XIII.  THE  VELOCITY  OF  CHEMICAL  REACTION      .        .        .  276 

XIV.  ELECTROMOTIVE  FORCE 307 

INDEX 322 

vii 


PHYSICAL    CHEMISTRY 


CHAPTER  I 

GASES   FROM    THE   STANDPOINT    OF   EXPERIMENT    AND 
THEORY.       DIFFUSION    PHENOMENA 

THE  recent  development  of  physical  chemistry  has  been  char- 
acterised very  specially  by  the  elaboration  and  application 
of  new  methods  for  the  study  of  the  phenomena  exhibited 
by  solutions.  These  methods  are  closely  related  to  a  theory 
of  solution,  which  in  its  turn  is  rooted  in  the  ana-logy  ex- 
isting between  the  behaviour  of  solutions  and  that  of  gases. 
Any  attempt,  therefore,  to  expound  the  properties  of  solu- 
tions, and  the  interpretations  of  these  properties  that  have 
been  proposed,  must  be  preceded  by  a  glance  at  certain 
features  which  characterise  the  gaseous  state,  and  at  various 
theories  which  bear  on  the  nature  of  gases. 

Fundamental  Experimental  Laws. — For  physico- 
chemical  purposes  the  fundamental  facts  in  which  the 
behaviour  of  gases  is  revealed  are  summed  up  in  three 
laws,  two  of  which  are  purely  physical  in  character,  while 
the  third  is  more  accurately  described  as  chemical.  It  is 
perhaps  necessary  to  emphasise  the  fact  that  these  three 
laws  are  absolutely  independent  of  any  theories  regarding 
the  nature  of  gases ;  they  are  simply  the  integrated  ex- 
pression of  experimental  results. 

(a)  Boyle's  Law. — According  to  this  law,  the  volume 

A 


;  V  '  :  '•  : 
2,-      .  .:  ...  r*  PHYSICAL   CHEMISTRY 

occupied  by  a  give'n  mass'  of  gas  varies  inversely  as  tl 
pressure  to  which  it  is  subjected,  provided  the  temperatui 
is  kept  constant.  The  algebraic  expression  of  this  relatioi 
ship  is  pv  =  C,  where  p  is  the  pressure,  v  is  the  volnnn 
^  and  C  is  a  constant.  This  is  the  equation  to  a  hyperboL 
and  the  curve  therefore  representing  the  correspondin 
changes  of  pressure  and  volume  for  a  given  quantity  ( 
a  gas  at  constant  temperature  belongs  to  this  type.  ] 
we  represent  by  vl  the  volume  occupied  by  a  give 
quantity  of  gas  under  the  pressure  pv  and  by  vz  il 
volume  at  the  same  temperature  under  the  pressure  p 
then  we  may  express  Boyle's  law  by  the  formul 
P1v1=p2v2.  As  an  instance  of  the  extent  to  which  th: 
law  has  been  verified  in  work  of  the  most  accurate  kin( 
Lord  Rayleigh's  figures  for  hydrogen,  oxygen,  and  carko 
dioxide  may  be  quoted.1  He  has  shown  that  if  the  valu 
of  pv  obtained  for  p  =  1  atmosphere  is  taken  as  unity 
then  the  value  of  pv  for  p  =  Q'5  atmosphere,  instead  c 
1-0000,  is  found  to  be  0-99974  in  the  case  of  hydrogei 
1-00038  in  the  case  of  oxygen,  and  1-00279  in  the  cas 
of  carbon  dioxide.  For  ordinary  gases  and  under  ordinal- 
conditions,  therefore,  Boyle's  law  may  be  taken  as  a 
accurate  statement  of  the  corresponding  variation  c 
pressure  and  volume. 

Under  certain  conditions,  however,  the  formula  pv  =  \ 
ceases  to  represent  accurately  the  behaviour  of  a  gas  a 
constant  temperature,  and  hence  it  must  be  regarde 
as  of  only  limited  validity.  Such  deviations  from  stric 
•  obedience  to  Boyle's  law  occur  (1)  when  the  pressur 
applied  to  the  gas  is  very  high,  and  (2)  when  the  ga 
is  near  its  point  of  condensation.  Amagat,  for  instance 
in  his  experiments  2  on  the  compressibility  of  nitrogen  a 
22°,  found  that  if  the  value  of  pv  for  p=~L  atmospher 

1  See  Phil  Trans.,  A,  1905,  204,  351. 

2  Ann.  chim.  phys.   (5),^880,  19,  345. 


GASES  3 

is  taken  as  unity,  the  value  for  ^==62  atmospheres  is 
as  low  as  0'986,  while  for  p  =  373*3  atmospheres  it  is 
as  high  as  1-207.  Such  deviations  from  Boyle's  law, 
however,  become  in  all  cases  less  marked  at  highei 
temperatures. 

(b)  Gay-Lussac 's  Law. — The  volume  occupied  by  a  given 
mass  of  gas,  kept  under  constant  pressure,  increases  as 
its  temperature  is  raised,  and  the  relative  expansion  is 
approximately  the  same  for  all  gases.  It  is  found  that 
for  1°  0.  rise  of  temperature  the  volume  of  a  gas  increases 
by  -j-f^  of  the  volume  which  it  occupies  at  0°  0.,  subject 
to  the  condition  that  the  pressure  remains  the  same 
during  the  rise  of  temperature.  If  VQ  and  v  are  the 
volumes  occupied  by  a  given  mass  of  gas  at  0°  C.  and 
£°  C.  respectively  under  equal  pressures,  and  if  a  =  Y|^  re- 
presents the  coefficient  of  expansion  common  to  all  gases, 
then  Gay-Lussac's  law  may  be  expressed  algebraically  by 
the  equation  v  =  v0(  I  +  at). 

From  the  foregoing,  taken  in  conjunction  with  Boyle's 
law,  it  is  easy  to  show  that  the  pressure  exerted  by  a 
given  mass  of  gas  kept  at  constant  volume  must  increase 
with  rising  temperature  in  the  same  proportion  as  the 
volume  increases  at  constant  pressure ;  so  that,  if  p0  and 
p  represent  the  pressure  at  0°  C.  and  t°  C.  respectively, 
P=PQ(\.  +  at),  subject  to  the  condition  that  the  volume 
of  the  gas  remains  the  same  throughout.  This  formula 
is  not  only  deducible  from  the  equations  pv  =  G  and 
v  =  vQ(l.  +  at),  but  is  also  in  harmony  with  the  results 
of  experimental  work. 

The  formula  pv  =  C  is  applicable  only  when  the  tem- 
perature is  constant,  and  the  formula  v  =  v0(l+at)  only 
when  the  pressure  is  constant ;  but  since  the  final  con- 
dition of  a  gas  may  differ  from  its  initial  condition  in 
respect  both  of  temperature  and  of  pressure,  it  is  obvious 
that  there  must  be  also  some  one  equation  connecting  the 


4  PHYSICAL   CHEMISTRY 

initial  and  the  final  volumes  in  this  case.  This  equatioi 
may  be  deduced  easily  in  the  following  manner.  W< 
may  suppose  that  a  given  quantity  of  a  gds,  occupying 
the  volume  VQ  at  the  pressure  p0  and  the  temperatun 
0°  C.,  occupies  the  volume  v  at  the  pressure  p  and  th( 
temperature  t°  C.  ;  the  problem,  then,  is  to  find  th( 
algebraic  relationship  between  v  and  v0.  If  we  stan 
with  the  gas  at  0°  and  raise  its  temperature  to  £°,  the 
pressure  being  kept  constant,  the  new  volume  v1  occupied 
by  the  gas  can  be  easily  calculated,  for  these  simultaneous 
changes  of  volume  and  temperature  are  subject  to  Gay- 
Lussac's  law;  that  is,  v1  =  v0(l-\-at).  If  now,  at  the 
temperature  t°,  we  alter  the  pressure  from  pQ  to  p,  the 
volume  changes  from  vt  to  V,  which  we  have  chosen  tc 
represent  the  final  volume.  To  simultaneous  changes  oi 
pressure  and  volume  at  constant  temperature  Boyle's  law 
is  applicable,  so  that  we  have  pv  =p<pi  =^ovo(  ^  +  aO- 
This  equation,  pv=p0v0(l  +  at),  is  the  algebraical  ex- 
pression both  of  Boyle's  law  and  of  Gay-Lussac's  law. 
Its  validity  is  not  absolute,  inasmuch  as  gases  exhibit 
deviations  from  strict  obedience  to  Gay-Lussac's  law  as 
well  as  Boyle's  law. 

If  the  numerical  value  of  the  coefficient  a  is  inserted 

in  the  equation  it  assumes  the  form  pv=p0v0--  ;   if, 


further,  it  is  agreed  to  reckon  temperature,  not  from 
0°  C.,  but  from  a  point  273  degrees  lower,  and  to  take 
T  as  the  symbol  of  temperature  on  this  new  scale,  then 
the  equation  may  be  written  pv=~~T.  Temperature 
reckoned  in  this  way  is  known  as  '  absolute  '  temperature, 
and  —  273°  C.,  the  starting  point  of  the  '  absolute  '  scale, 
is  termed  the  '  absolute  '-zero. 

The  equation  pv  =  ^^T  sums  up  the  physical  be- 
haviour of  gases  so  far  as  that  is  defined  by  the  laws 
of  Boyle  and  Gay-Lussac,  but  for  certain  purposes  it  is 


GASES  5 

desirable  to  have  the  direct  relationship  between  vv  the 
volume  which  a  quantity  of  gas  occupies  at  pressure  pl 
and  absolute  temperature  Tv  and  vz,  the  volume  which 
it  occupies  at  pressure  p2  and  absolute  temperature  T2 
A  little  consideration  of  the  foregoing  equation  will  show 

that  the  relationship  required  is  %?  =  TJ?. 

-*1  ^2 

(c)  Gay-Lussacs  Law  of  Volumes. — This  third  experi- 
mental law,  although  associated  with  the  same  name  as 
the  second  law,  is  purely  chemical  in  its  character,  and 
deals  with  the  relative  proportions  by  volume  in  which 
chemical  reaction  between  gases  takes  place.  The  law 
states  that  when  two  gases  combine  with  each  other  to 
form  a  third  gas,  the  volumes  of  the  reacting  gases  are 
in  a  simple  ratio  to  one  another  and  to  the  volume  of 
the  gaseous  product  (all  volumes  being  measured  at  the 
same  temperature  and  pressure).  Special  cases  of  this 
will  doubtless  occur  to  the  reader;  it  is,  for  instance, 
well  known  that  1  volume  of  hydrogen  combines  with 
1  volume  of  chlorine  to  form  2  volumes  of  hydrogen 
chloride,  and  that  2  volumes  of  hydrogen  combine  with 
1  volume  of  oxygen  to  form  2  volumes  of  water  vapour. 

No  gas  is  absolutely  'perfect,'  that  is,  no  gas  con- 
forms rigidly  to  the  first  two  laws,  and  hence  it  follows 
that  the  volume  ratio  of  reacting  gases  found  in  the 
most  accurate  experimental  work  is  less  simple  than  the 
preceding  paragraph  would  seem  to  indicate.  At  0°  C. 
and  760  mm.,  for  instance,  the  ratio  of  the  volumes  of 
hydrogen  and  oxygen  uniting  to  form  water  is  2*0028 : 1, 
according  to  Scott's  accurate  investigations.1  If,  however, 
a  correction  is  made  for  the  slight  extent  to  which 
hydrogen  and  oxygen  deviate  from  Boyle's  law  (see 
p.  2),  the  volume  ratio  is  almost  exactly  2:1. 

1  Phil.   Trans.,  1893,  A,  184,  543.     See  also  Morley,  Zeit.  physical. 
Chem.,  1896,  20,  417. 


6  PHYSICAL  CHEMISTEY 

Theories  bearing  on  the  Nature  of  Gases.—  (a)  7%< 

Kinetic  Theory  of  Gases.  —  A  little  consideration  of  th< 
experimental  laws  which  have  just  been  enunciated  showi 
that  gases  are  characterised  by  simplicity  and  uniformity 
both  in  their  physical  behaviour  and  in  their  chemica 
relationships.  Various  theories  have  been  brought  for- 
ward which  offer  an  interpretation  of  this  simple  anc 
uniform  behaviour.  According  to  one  of  these,  the 
kinetic  gas  theory,  the  ultimate  particles  of  a  gas  ar< 
rushing  about  at  a  high  speed,  the  direction  of  thei] 
motion  being  altered  only  when  they  collide  with  one 
another  or  impinge  on  the  walls  of  the  containing  vessel 
The  velocity  of  motion  will  vary  somewhat  from  one 
particle  to  another,  but  so  long  as  the  temperature  oJ 
a  mass  of  gas  remains  the  same,  the  average  velocity  o1 
the  constituent  particles  will  be  constant.  The  pressure 
exerted  by  the  gas  is  due  to  the  impacts  delivered  or 
the  walls  of  the  containing  vessel  by  the  moving  particles 
If  it  is  further  assumed  that  the  volume  of  the  particles 
themselves  is  negligible  compared  with  the  total  volume 
of  the  gas,  and  that  they  are  perfectly  elastic,  it  follow* 
by  the  principles  of  mechanics  that  at  constant  tem- 
perature pv  =  ^mnu2,  in  which  equation  m  is  the  mass 
of  an  individual  particle  of  the  gas,  n  is  the  number  oJ 
particles  in  volume  v  of  the  gas,  and  u  is  the  average 
velocity  of  the  molecules  at  the  temperature  considered, 
So  long  as  the  temperature  is  unchanged  the  producl 
fynnu2  has  a  constant  value,  hence  pv  =  const.,  which 
is  the  algebraic  expression  of  Boyle's  law.  The  assump- 
tions of  the  kinetic  gas  theory,  then,  involve  the  relation 
between  pressure  and  volume  required  by  the  first  fun- 
damental law  of  gases.  If  the  temperature  is  changed. 
then  the  value  of  pv  for  a  given  mass  of  gas  alters 


according  to  the  formula  already  discussed  —  Pv=lT,  ori 


GASES  7 

in  words,  the  product  of  pressure  and  volume  is  pro- 
portional to  the  absolute  temperature.  But,  according 
to  the  kinetic  theory,  pv  =  %mnu2,  and,  if  we  are  dealing 
throughout  with  the  same  quantity  of  a  given  gas,  the 
values  of  m  and  n  are  independent  of  temperature,  so 
that  u2  must  be  proportional  to  the  absolute  temperature. 
The  kinetic  gas  theory  involves  therefore  a  definite  con- 
ception of  what  happens  when  the  temperature  of  a  gas 
is  raised ;  the  kinetic  energy  of  the  molecules  increases 
proportionally  to  the  absolute  temperature. 
v(5)  Avogadro's  Hypothesis. — According  to  this  hypo- 
thesis, which  bears  especially  on  the  third  experimental 
law,  equal  volumes  of  different  gases,  measured  at  the 
same  temperature  and  pressure,  contain  the  same  number 
of  ultimate  particles  or  molecules.  If  it  is  supposed  that 
when  two  gases  combine  chemically  one  ultimate  particle 
of  the  first  gas  reacts  with  one,  two,  or  three  ultimate 
particles  of  the  second  gas,  then  Avogadro's  hypothesis 
is  seen  to  offer  a  plausible  and  natural  interpretation  of 
Gay-Lussac's  Law  of  Volumes.  But  the  essential  point 
of  the  hypothesis,  as  it  was  enunciated  by  Avogadro, 
lay  in  the  distinction  which  he  drew  between  atoms 
and  molecules.  He  suggested  that  the  molecule  of  an 
element  was  not  necessarily  the  same  as  the  atom,  and 
that  the  ultimate  particle  of  a  gaseous  element  might 
contain  one,  two,  or  more  atoms  of  that  element.  Only 
when  this  suggestion  is  adopted  is  Avogadro's  hypothesis 
capable  of  interpreting  all  the  special  cases  which  are 
summarised  in  Gay-Lussac's  law. 

Avogadro's  hypothesis  was  brought  forward  primarily 
as  offering  an  explanation  of  the  volume  relationships  of 
chemically  reacting  gases,  but  it  obviously  furnishes  also 
a  simple  interpretation  of  the  uniform  behaviour  of  dif- 
ferent gases  when  exposed  to  changes  of  pressure  and 
temperature.  It  is  noteworthy  also  that  the  hypothesis 


8  PHYSICAL   CHEMISTRY 

is  found  to  be  in  harmony  with  the  consequences  of  th( 
kinetic  gas  theory. 

The  proposition  advanced  by  Avogadro  has  beer 
adopted  as  a  working  hypothesis,  and  as  such  has  stooc 
the  test  of  time ;  it  is,  in  fact,  a  necessary  supplement  t( 
the  Atomic  Theory.  Since  the  hypothesis  is  closely  con- 
nected with  much  that  is  to  follow,  it  is  essential  tc 
indicate  at  this  stage  the  results  that  flow  directly  froir 
its  acceptance. 

First  of  all,  the  acceptance  of  Avogadro's  hypothesis 
leads  to  a  definite  conception  of  the  relation  betweer 
the  atom  and  the  molecule  of  the  gaseous  elements 
The  argument  may  be  stated  as  follows.  It  is  a  recog- 
nised experimental  result  that  1  volume  of  hydroger 
unites  with  1  volume  of  chlorine  to  form  2  volumes  oJ 
hydrogen  chloride.  If  now  we  suppose  that  1  volume 
of  hydrogen  contains  n  ultimate  particles  of  hydrogen 
then,  according  to  Avogadro,  the  1  volume  of  chlorine 
also  contains  n  ultimate  particles  of  chlorine,  whilst  the 
2  volumes  of  the  product  contain  2n  ultimate  particles 
of  hydrogen  chloride ;  that  is,  n  ultimate  particles  oi 
hydrogen  unite  with  n  ultimate  particles  of  chlorine  tc 
form  2n  ultimate  particles  of  hydrogen  chloride.  Since 
we  cannot  conceive  of  an  ultimate  particle  of  hydrogen 
chloride  which  does  not  contain  at  least  one  atom  oi 
hydrogen,  the  n  ultimate  particles  of  hydrogen  musl 
have  contained  at  least  2n  atoms.  Hence  each  ultimate 
particle,  or  molecule,  of  hydrogen  must  contain  at  least 
two  atoms.  There  are  grounds,  which  cannot  be  dis- 
cussed here,  for  supposing  that  the  molecule  of  hydrogen 
does  not  contain  more  than  two  atoms;  hence  we  must 
conclude  that  the  molecule  of  hydrogen  contains  two  atoms. 

The  argument  may  be  similarly  stated  in  the  case  oi 
other  gaseous  elements. 

Secondly,    the    acceptance    of    Avogadro's    hypothesis 


GASES  Q 

leads  to  a  definite  relationship  between  density  and 
molecular  weight.  Suppose  that  D  is  the  density  of 
a  gas,  and  that  M  is  the  weight  of  one  molecule :  let 
DH  and  MH  represent  the  corresponding  quantities  for 
hydrogen.  Suppose  also  that  in  unit  volume  of  the 
gas  at  N.T.P.  (that  is,  at  normal  temperature  and  pres- 
sure— 0°  C.  and  1  atmosphere)  there  are  n  molecules; 
then,  according  to  Avogadro,  unit  volume  of  hydrogen 
at  N.T.P.  also  contains  n  molecules.  Now  the  ratio  of 
the  densities  of  two  gases  is  equal  to  the  ratio  of  the 
weights  of  equal  volumes  of  the  two  gases,  measured 
of  course  at  the  same  temperature  and  pressure ;  hence 
D  _ Weight  of  unit  volume  of  the  gas  at  N.T.P._  n.M  _  M 
Du~~  Weight  of  unit  volume  of  hydrogen  at  N.T.P.  ~ n.MH~~ Ma' 

As  has  been  already  shown,  the  molecule  of  hydrogen 
contains  two  atoms,  and  therefore  the  value  of  MH  is 
twice  the  atomic  weight.  On  the  basis  of  0  =  16,  the 
atomic  weight  of  hydrogen  is  1*008,  so  that  Jl/#=  2*016. 
If,  further,  it  is  agreed  to  refer  the  density  of  gases 
and  vapours  to  that  of  hydrogen  taken  as  unity,  then 
DH  —  \,  and  we  have  Jf=2'016Z>.  In  words,  the  mole- 
cular weight  of  a  gas  is  approximately  equal  to  twice  its 
density  (relatively  to  hydrogen). 

Thirdly,  the  adoption  of  Avogadro 's  hypothesis  permits 
us  to  cast  the  equation  pv=^~T  into  a  more  general 
form,  although  it  should  be  borne  in  mind  that  in  so 
doing  we  are  introducing  a  hypothetical  element  into 
what  is  otherwise  an  expression  of  purely  experimental 
laws.  It  is  obvious  that  if  we  take  weights  of  two  gases 
in  the  ratio  of  their  molecular  weights,  we  are  taking 
an  equal  number  of  molecules  in  the  two  cases,  which 
means,  according  to  Avogadro's  hypothesis,  that  we  are 
taking  equal  volumes  (measured,  naturally,  at  the  same 
temperature  and  pressure).  Hence,  if  we  are  dealing 
with  the  molecular  weight  in  grams  of  any  gas,  a  gram- 


10  PHYSICAL   CHEMISTRY 

molecule,  or  '  mol '  as  it  is  called,  the  volume  occupied 
at  1  atmosphere  and  0°  C.  should  always  be  the  same. 
This  gram-molecular  volume  must  be  the  volume  occupied 
at  1  atmosphere  and  0°C.  by  2*016  grams  of  hydrogen  or  32 
grams  of  oxygen,  and  that  has  been  found  to  be  224  litres. 
If,  then,  it  is  agreed  that  in  applying  the  equation 

p^  —  ^-^T  the  quantity  of  gas  considered  is  always  1  gram- 
molecule,  the  value  of  v0  for  p0=l  is  the  same  in  all  cases. 
Hence  the  equation  may  be  written^— JRT,  where  ^=§S 

is  a  constant  for  all  gases.  The  actual  numerical  value  of 
R  depends  on  the  units  in  which  the  pressure  and  volume 
are  measured ;  if,  for  instance,  pressure  is  measured  in  atmo- 

1  x  22*4 
spheres  and  volume  in  litres,  then  R=         —  =  -082. 

At  6 

The  equation  pv  —  ET  is  termed  the  gas  equation,  and 
is  of  the  utmost  importance,  not  only  in  connection  with 
gases,  but  also  in  relation  to  the  behaviour  of  dissolved 
substances,  as  will  appear  later.  Whenever  the  equation 
is  applied,  it  is  understood  that  1  gram-molecule  of  the 
substance  is  being  considered. 

Determination  of  the  Molecular  Weight  of  Gases  and 
Yapours. — As  has  already  been  pointed  out,  the  accept- 
ance of  Avogadro's  proposition  as  a  working  hypothesis 
leads  to  a  definite  relationship  between  molecular  weight 
and  density,  expressed  by  the  equation  M  =  2-Q16D,  D  being 
the  density  of  the  gas  relatively  to  hydrogen.  The  deter- 
mination of  molecular  weight  resolves  itself  therefore  into  a 
determination  of  density,  and  it  is  necessary  to  consider  at 
least  two  of  the  practical  methods  available  for  this  purpose. 

Regnault's  Method. — Two  spherical  glass  bulbs,  each 
provided  with  narrow  tube  and  stopcock,  and  of  approxi- 
mately equal  volume,  are  required.  The  one  is  used 
merely  as  a  counterpoise  on  the  balance,  the  other  is 
weighed  (a)  when  completely  evacuated,  (5)  when  filled 


GASES 


11 


at  known  temperature  and  pressure  with  the  gas  under 
examination.  The  volume  of  the  second  bulb  having 
been  deduced  from  the  quantity  of  water  or  mercury 


FIG.  l. 


which  it  contains, 
the  difference  of 
the  weights  (a) 
and  (b)  is  the 
weight  of  a  known 
volume  of  the  gas 
at  known  tempera- 
ture and  pressure. 
From  these  data 
it  is  easy  to  cal- 
culate the  weight 
of  1  cub.  cm.  of 
the  gas  at  N.T.P., 
and  the  result  so 
obtained  is  com- 
pared with  the  cor- 
responding figure 
for  hydrogen. 
Victor  Meyer's 


Method. — While  Eegnault's  method  is  specially  applicable 
to  substances  which  are  gases  at  the  ordinary  tempera- 
ture, this  second  method  is  employed  in  the  case  of 


12  PHYSICAL   CHEMISTRY 

substances  which  are  normally  liquid,  but  can  be  vaporised 
without  difficulty. 

The  necessary  apparatus  is  sketched  in  the  preceding 
diagram  (Fig.  1).  The  glass  tube  A  with  cylindrical 
bulb  B  and  the  two  side  tubes  C  and  D  is  suspended 
in  the  wide  vessel  E,  so  that  the  end  of  the  bulb  B  is  a 
short  distance  above  the  surface  of  the  liquid  which 
occupies  the  bottom  of  E.  The  glass  rod  F,  which  is 
pushed  through  the  side  tube  C,  is  kept  in  position  by 
indiarubber  tubing ;  the  elasticity  of  the  latter  allows 
F  to  be  temporarily  pulled  clear  of  A  without  any  dis- 
turbance of  its  permanent  position.  The  end  of  the 
other  side  tube  D  is  placed  under  a  graduated  tube  full 
of  water  standing  in  the  vessel  G.  When  the  apparatus 
has  been  set  up  the  liquid  in  E  is  boiled  and  the  rate 
of  ebullition  is  adjusted,  so  that  ultimately  the  greater 
part  of  the  tube  E  is  filled  with  vapour;  the  liquid  in 
E  must  have  a  boiling  point  at  least  20°  above  that  of 
the  liquid  the  vapour  density  of  which  is  being  deter- 
mined. The  boiling  of  the  liquid  in  E  will  obviously 
expel  a  certain  amount  of  air  from  the  bulb  B  and  the 
tube  A,  but  ultimately,  when  the  ebullition  is  steady, 
the  expulsion  of  air  will  cease,  and  there  will  .be  tem- 
perature equilibrium  between  the  inner  vessel  and  the 
surrounding  vapour.  This  state  of  equilibrium  has  been 
reached  when  after  the  insertion  of  a  stopper  in  the  top 
of  the  tube  A  no  bubbles  of  air  are  expelled  through  D. 

A  small  bottle  containing  a  weighed  quantity  of  the 
liquid  under  examination  is  then  dropped  through  the 
top  of  A  on  to  the  end  of  F,  and  the  stopper  is  re-inserted. 
When  the  rod  F  is  pulled  back  for  a  moment  the  bottle 
falls  to  the  bottom  of  B,  in  which  a  little  glass  wool 
has  previously  been  placed  to  prevent  fracture.  At  the 
temperature  which  prevails  in  B  the  liquid  is  rapidly 
vaporised  and  a  corresponding  quantity  of  air  is  expelled 


GASES  13 

in  successive  bubbles  from  the  end  of  D.  The  air  thus 
collected  in  H  is  the  exact  equivalent  of  the  vapour 
produced  in  B,  and  when  no  more  bubbles  are  expelled, 
its  volume  is  found  by  transferring  H  to  a  cylinder  full 
of  water  and  measuring  at  known  temperature  and  pressure 
in  the  usual  way.  Since  this  volume  of  vapour  has  been 
produced  from  the  known  weight  of  the  liquid  taken,  the 
weight  of  1  cub.  cm.  of  the  vapour  at  N.T.P.  may  easily 
be  calculated  ;  the  density  is  then  obtained  by  comparing 
this  result  with  the  corresponding  figure  for  hydrogen. 

An  example  may  be  taken  to  show  how  the  data  obtained 
in  an  experiment  with  Victor  Meyer's  apparatus  are  used 
to  calculate  the  density,  and  from  that  the  molecular 
weight.  In  a  particular  case  0*1  gram  of  a  substance  was 
weighed  out  and  vaporised  in  a  Victor  Meyer  apparatus. 
The  expelled  air  was  collected  over  water  and  found  to 
measure  32  cub.  cm.  at  17°  C.  and  750  mm.  pressure. 
Now  the  tension  of  aqueous  vapour  at  17°  is  14*4  mm., 
and  the  volume  of  air  expelled,  when  allowance  has 

,     r       ,,  .  .         ,  32  X  273  X  (750  -14'4) 

been  made  for  this  tension,  becomes    -     —  290  x  760  — 

=  29-16  cub.  cm.  at  N.T.P.  This,  then,  would  be  the 
volume  of  vapour  produced  if  O'l  gram  of  the  substance 
were  vaporised  at  N.T.P.,  and  it  follows  that  the  weight 

of  1  cub.  cm.  of  the  vapour  at  N.T.P.  would  be  gram. 


The  weight  of  1  cub.  cm.  of  hydrogen  under  these  con- 
ditions is  '00009  gram,  and  therefore  the  density  of  the 

vapour  (relatively  to  hydrogen)  is  29.16x.00009  =  38'1  5  tne 
molecular  weight   is  then  38'1  X  2'016  =  76'8. 

Gaseous  Diffusion.  —  One  characteristic  feature  of  a  gas 
as  compared  with  a  liquid  or  a  solid  is  its  ability  to 
occupy  fully  any  space  which  is  offered  to  it  ;  it  is  capable 
of  infinite  expansion,  and  more  than  that,  the  occupation  of 
any  vacant  space  by  a  gas  is  accomplished  with  great 


14  PHYSICAL   CHEMISTRY 

rapidity.  Again,  when  two  vessels  containing  two  dif- 
ferent gases  at  the  same  pressure  are  put  into  com- 
munication with  each  other,  a  process  of  diffusion  goes 
on  until  the  composition  of  the  gaseous  mixture  is  the 
same  at  all  points.  Each  gas  moves  from  places  where 
its  concentration  is  high  to  places  where  its  concentration 
is  low,  and  equilibrium  is  not  attained  until  the  partial 
pressure  of  each  gas  is  the  same  throughout.  Such 
diffusion  or  mutual  interpenetration  is  quite  distinct  from 
movement  of  the  gas  as  a  whole.  A  difference  of  gas 
pressure  in  two  places  may  be  equalised  by  mass  move- 
ment— air  currents,  for  example — but  diffusion  goes  on 
where  such  movement  is  excluded ;  it  is  a  molecular  process. 

The  kinetic  gas  theory,  which  has  so  far  been  discussed 
only  in  its  bearing  on  Boyle's  law  and  Gay-Lussac's 
law,  supplies  a  plausible  interpretation  of  these  diffusion 
phenomena.  If,  as  the  theory  supposes,  each  molecule 
is  moving  at  a  high  speed  (a  mile  per  second,  more  or 
less,  according  to  the  density  and  the  temperature  of 
the  gas),  it  is  intelligible  that  a  gas  brought  in  contact 
with  a  vacuous  space  should  occupy  the  latter  practically 
instantaneously.  On  the  other  hand,  when  one  gas  is 
diffusing  into  another  gas  the  rate  of  advance  is  naturally 
much  slower,  for  the  forward  path  of  each  molecule,  on 
account  of  the  frequent  collisions  with  the  molecules 
of  the  other  gas,  is  of  a  zigzag  character. 

One  of  the  conclusions  which  can  be  deduced  from 
the  assumptions  of  the  kinetic  gas  theory  is  that  the 
velocity  with  which  a  gaseous-  molecule  is  endowed  is 
inversely  proportional  to  the  square  root  of  the  density 
of  the  gas.  It  follows  from  this,  for  instance,  that  the 
hydrogen  molecule  has  a  velocity  four  times  as  great 
as  that  of  the  oxygen  molecule  at  the  same  temperature, 
for  oxygen  is  sixteen  times  as  heavy  as  hydrogen.  If, 
then,  we  are  correct  in  suggesting  that  diffusion  pheno- 


GASES  15 

mena  are  closely  related  to  molecular  velocity,  we  may 
expect  to  find  a  definite  connection  between  the  rate 
of  diffusion  and  the  density  of  a  gas.  In  circumstances 
where  the  molecular  movement  alone  comes  into  play, 
the  rate  of  diffusion  of  a  gas  ought  in  fact  to  be  inversely 
proportional  to  the  square  root  of  its  density. 

This  important  relationship  was  verified  by  Graham1 
in  his  experiments  on  the  rate  of  passage  of  different 
gases  through  minute  apertures  into  a  vacuum.  The 
experiments  consisted  in  determining  the  times  required 
for  a  given  volume  of  various  gases  kept  at  steady 
pressure  to  pass  through  a  minute  perforation  in  a  metal 
plate  into  a  receiver  which  was  being  constantly  eva- 
cuated. Graham  found  that  the  time  required  for  the 
escape,  or  '  effusion '  as  he  called  it,  of  a  given  volume  of 
any  gas  was  proportional  to  the  square  root  of  its  density ; 
in  other  words,  the  velocity  of  effusion  of  a  gas  is  in- 
versely proportional  to  the  square  root  of  its  density. 

Some  of  Graham's  results  are  recorded  in  the  accom- 
panying table.  The  times  necessary  for  the  effusion  of 
a  certain  volume  of  gas  are  given  in  the  second  column, 
while  in  the  third  column  are  the  figures  calculated  on 
the  assumption  that  the  time  of  effusion  is  proportional 
to  the  square  root  of  the  density ;  in  both  cases  the 
time  required  for  the  effusion  of  air  is  taken  as  unity. 

Time  of  Effusion. 

Gas.  Experiment.  Theory. 

Air 1  1 

Nitrogen 0'984  0-986 

Oxygen 1'050  1'052 

Hydrogen 0-276  0-263 

Carbon  Dioxide  ....  M97  1-237 

This  relationship  has  been  confirmed  by  Bunsen,2  who  has 
further  based  on  it  a  method  for  the  approximate  deter- 
mination of  the  density  of  a  gas. 

1  Graham,  Chemical  and  Physical  Researches,  p.  95.      2  Gasometry,  p.  121. 


16  PHYSICAL   CHEMISTRY 

The  rate  of  passage  of  a  gas  through  a  capillary  tube 
into  a  vacuum  is  not  inversely  proportional  to  the  square 
root  of  the  density ;  the  friction  at  the  interior  surface 
of  the  tube  comes  in  as  a  disturbing  factor.  The  velocity 
of  diffusion  of  one  gas  into  another  through  a  porous 
diaphragm  is  inversely  proportional  to  the  square  root  of 
the  density  only  when  the  diaphragm  is  extremely  thin. 

Static  Diffusion  of  Carbon  Dioxide. — Another  in- 
teresting phenomenon  in  the  same  field  as  the  fore- 
going is  the  diffusion  of  a  gas  through  a  tube,  at  one 
end  of  which  its  concentration  is  kept  either  at  zero  or 
at  some  constant  low  value.  This  case  is  interesting 
because  of  its  bearing  on  the  absorption  of  carbon  dioxide 
at  the  surface  of  a  leaf. 

The  gas  exchange  between  the  atmosphere  and  the 
assimilating  cells  of  a  leaf  is  at  one  stage  simply  a 
process  of  diffusion  through  the  stomata  alone,  for  Black- 
man  has  shown l  that  if  these  are  blocked  up  no  appreci- 
able diffusion  of  carbon  dioxide  into  the  leaf -takes  place. 
This  being  so,  the  diffusion  of  carbon  dioxide  through 
the  stomata  must  be  relatively  rapid;  indeed,  in  the 
case  of  a  certain  leaf  examined  by  Brown  and  Escombe 2 
the  stomatic  openings  were  found  to  absorb  per  sq.  cm. 
of  their  area  as  much  as  7*77  cub.  cm.  of  carbon  dioxide 
per  hour,  a  figure  which  is  about  fifty  times  as  great 
as  the  absorption  per  unit  area  of  a  freely  exposed  solution 
of  caustic  alkali.  The  question  whether  this  was  possible 
led  Brown  and  Escombe  to  study  the  free  diffusion  of 
carbon  dioxide  through  small  apertures  into  cavities  with 
a  comparatively  large  absorbing  surface. 

These  investigators  found  that  if  a  tall  cylinder  com- 
municating freely  with  the  atmosphere  contains  at  the 

1  Phil.  Trans.,  B,  1895,  186,  485,  503. 

2  Ibid.,  B,  1900,  193,  223.  - 


17 

bottom  a  layer  of  caustic  alkali,  there  is  a  regular  flow 
or  drift  of  carbon  dioxide  down  the  cylinder.  Provided 
that  the  air  outside  the  cylinder  is  of  uniform  com- 
position, and  the  air  inside  is  free  from  convection 
currents,  a  static  condition  of  affairs  is  established 
analogous  to  what  is  observed  when  one  end  of  a  metal 
bar  is  kept  at  a  high  temperature  and  the  other  end 
at  a  low  temperature.  When  the  steady  condition  of 
diffusion  has  been  attained  the  rate  of  flow  of  the 
carbon  dioxide,  as  deduced  from  the  amount  absorbed, 
is  found  to  be  inversely  proportional  to  the  length  of 
the  diffusion  column.  This  is  what  might  be  expected 
on  general  grounds,  for  the  gradient  of  the  line  joining 
two  points  of  fixed  different  altitude  diminishes  as  the 
distance  between  the  two  points  increases. 

When  now  a  diaphragm  with  a  circular  aperture  is 
placed  at  the  free  end  of  the  diffusion  column,  the  pro- 
cess of  diffusion  and  absorption  is  modified  in  a  re- 
markable manner.  As  the  size  of  the  aperture  is 
diminished,  the  diffusive  flow  per  unit  area  of  aperture 
increases  rapidly,  and  when  the  area  of  the  aperture 
has  become  small  in  comparison  with  the  sectional  area 
of  the  tube,  the  amount  of  diffusing  gas  is  proportional 
to  the  diameter  of  the  aperture,  not,  as  one  might 
expect,  to  its  area.  This  bare  statement  of  results  is 
illustrated  by  the  following  figures  from  Brown  and 
Escombe's  paper: — 


Diameter 
of  Aperture 
in  mm. 

Carbon  Dioxide 
diffused  per 
Hour  in 
cub.  cm. 

COa  diffused 
per  sq.  cm. 
of  Aperture 
per  Hour  in 
cub.  cm. 

Ratio  of 
Areas  of 
Apertures. 

Ratio  of 
Diameters  of 
Apertures. 

Ratio  of 
Total  C02 
diffused 
per  Hour. 

22-7 

•2380 

•0588 

1-00 

1-00 

1-00 

12-06 

•0928 

•0812 

•28 

•53 

•39 

5-86 

•0556 

•2074 

•066 

•25 

•23 

3-23 

•0399 

•4855 

•023 

•14 

•16 

2-12 

•0261 

•8253 

•008 

•093 

•10 

These  figures  make  it   plain  that   the   diffusive   flow,. 


18  PHYSICAL  CHEMISTRY 

especially  in  the  case  of  the  smaller  apertures,  is  pro- 
portional, not  to  the  area  of  the  aperture,  but  to  its 
diameter.  A  similar  '  diameter  law '  has  been  estab- 
lished for  the  diffusion  of  water  vapour  into  flasks  con- 
taining concentrated  sulphuric  acid  as  absorbent,  and 
for  the  evaporation  of  water  through  narrow  apertures 
into  desiccated  air. 

Diffusion  through  a  Multi-perforate  Diaphragm. — 
When  a  diffusion  tube,  such  as  that  already  described, 
is  covered  with  a  diaphragm  containing  many  small 
apertures,  the  diffusive  flow  is  checked  to  a  remarkably 
small  extent.  In  Brown  and  Escombe's  experiments 
diaphragms  were  employed  containing  100  perforations 
(0*38  mm.  diameter)  per  sq.  cm.  of  diaphragm  surface. 
Although  the  area  of  the  apertures  was  in  this  case 
only  about  one-ninth  of  the  total  area  of  the  diaphragm, 
the  amount  of  diffusion  through  the  perforations  was  as 
great  as  when  there  was  no  diaphragm  at  all.  The 
obstruction,  therefore,  which  is  offered  to  a  diffusive 
flow  by  a  multi-perforate  diaphragm  may  be  nil,  and 
is  certainly  surprisingly  small.  This  striking  result  is 
to  be  referred  to  the  intensification  of  the  diffusive 
flow  which,  as  shown  by  the  figures  already  quoted, 
accompanies  the  gradual  decrease  of  aperture.  Provided 
that  the  perforations  in  a  multi-perforate  septum  are 
not  too  close,  each  aperture  acts  independently  of  the 
others,  according  to  the  diameter  law. 

The  surface  of  a  leaf,  regarded  as  a  purely  physical 
apparatus  for  the  diffusion  of  atmospheric  carbon  dioxide 
to  the  assimilating  centres,  resembles  a  multi-perforate 
diaphragm.  The  amount  of  carbon  dioxide,  then,  which 
enters  the  stomata  will  (1)  depend  on  the  gradient  of 
density,  and  therefore  on  the  extent  to  which  the  carbon 
dioxide  concentration  in  the  respiratory  cavity  approaches 
zero,  (2)  be  proportional  to  the-  linear  dimensions  of 


GASES  19 

the  stomatic  openings.  In  view  of  the  fact  that  the 
stoinatic  openings  are  elliptical  in  shape,  the  question 
may  be  raised,  What  is  the  linear  dimension  of  such 
an  aperture  ?  The  answer  is  based  on  a  study  of  evapora- 
tion from  circular  and  elliptical  surfaces  of  equal  area, 
and  is  to  the  effect  that,  so  far  as  diffusion  is  concerned, 
an  elliptical  tube  is  equivalent  to  a  cylindrical  tube 
having  the  same  area  of  cross-section.  As  regards  the 
gradient  of  density  in  connection  with  the  absorption 
of  carbon  dioxide  by  a  leaf,  the  conditions  will  be  most 
favourable  when  the  partial  pressure  of  the  atmospheric 
carbon  dioxide  at  the  surface  of  the  leaf  is  kept  constant 
by  a  moveme'nt  of  the  air.  If  the  leaf  is  in  perfectly 
still  air,  there  will  be  a  density  gradient  for  the  carbon 
dioxide  outside  the  stomatic  openings  also,  and  the  maxi- 
mum possible  absorption  of  the  gas  by  the  leaf  will  be 
somewhat  diminished. 

From  Brown  and  Escombe's  researches  on  the  leaf 
of  Hdianthus  annmis,  it  appears  that  the  actual  intake 
of  carbon  dioxide  is  only  a  small  fraction  of  the  amount 
which  the  diffusion  mechanism  of  the  leaf  surface,  re- 
garded as  a  multi-perforate  septum,  is  able  to  deliver. 
It  follows  that  the  partial  pressure  of  the  carbon  dioxide 
in  the  respiratory  cavity  can  be  only  slightly  less  than 
in  the  atmosphere  outside.  The  passage  of  carbon 
dioxide  from  the  air  to  the  assimilating  cells  is  probably 
most  retarded  at  the  walls  of  the  latter.  In  order  to 
penetrate  these  the  gas  must  pass  into  solution  in  the 
water  with  which  they  are  charged,  and  the  subsequent 
process  of  liquid  diffusion  is  very  slow  compared  with 
gaseous  diffusion. 


CHAPTER   II 

ABSORPTION    OF   GASES   BY    LIQUIDS 

Solubility  and  Absorption. — It  will  be  clear  from  the 
closing  paragraph  of  the  last  chapter  that  in  the  gas 
exchange  between  an  organism  and  the  atmosphere  there 
are  other  factors  involved  besides  gaseous  diffusion.  The 
gases,  both  those  which  are  being  absorbed  and  assimi- 
lated and  those  of  which  the  organism  is  ridding  itself, 
pass  into  solution  at  some  stage  or  other  of  the  exchange, 
and  the  facilities  for  such  an  exchange  will  therefore 
depend  on  the  extent  to  which  the  gases  are  soluble  in 
the  solvent  fluid. 

The  power  of  a  liquid  to  dissolve  a  gas  varies  very 
markedly  with  the  nature  of  the  gas,  and  the  solubility 
of  a  given  gas  in  a  given  liquid  depends  on  the  tem- 
perature and  the  pressure  at  which  the  absorption  takes 
place.  As  regards  the  first  of  these  factors,  it  is  found 
in  almost  all  cases  that  the  solubility  of  a  gas  in  a  liquid 
diminishes  as  the  temperature  rises.  The  relationship 
between  the  solubility  of  a  gas  and  the  pressure  under 
which  the  absorption  takes  place  is  comparatively  simple, 
and  is  embodied  in  Henry's  law. 

Henry's  Law. — According  to  this  law,  the  quantity 
of  a  gas  (either  weight,  or  volume  at  N.T.P.)  dissolved 
by  a  given  volume  of  a  given  liquid  at  a  given  tem- 
perature is  directly  proportional  to  the  pressure  under 
which  the  absorption  takes  place  ;^if,  for  instance,  the 


ABSORPTION   OF  GASES   BY   LIQUIDS      21 

pressure   on   the   gas   is  doubled,    twice   as   much  of  it 
will  be  forced  into  solution. 

With  what  accuracy  Henry's  law  represents  the  facts 
may  be  judged  from  the  numbers  in  the  following  table? 
which  refers  to  the  solubility  of  carbon  dioxide  in  water. 
P  is  the  pressure  (in  cm.  of  mercury)  under  which  the 
absorption  takes  place,  and  V  is  the  volume  of  carbon 
dioxide  (measured  at  N.T.P.)  which  is  absorbed  by  1  cub. 
cm.  of  water  at  15° ;  according  to  Henry's  law  the  ratio 

—  should  be  a  constant. 

* 

69-8  0-944  0-0135 

128-9  1-865  0-0144 

200-2  2-908  0-0145 

236-9  3-486  0-0147 

273-8  4-003  0-0146 

311-0  4-501  0-0145 

If  we  were  to  plot  the  weight  of  gas  dissolved  against 
the  pressure  under  which  the  absorption  takes  place,  then 
the  curve  obtained  in  the  case  of  a  gas  which  strictly 
obeys  Henry's  law  would  be  a  straight  line.  Deviation 
from  the  law  occurs  when  there  is  chemical  action  between 
the  gas  and  any  substance  present  in  the  absorbing  liquid 
In  such  a  case  the  relation  between  the  pressure  and  the 
quantity  of  gas  absorbed  is  not  a  linear  one.  If,  then, 
the  study  of  the  mutual  behaviour  of  a  gas  and  a  liquid 
shows  that  the  quantity  of  gas  absorbed  by  the  liquid  is 
not  a  linear  function  of  the  pressure,  it  may  safely  be 
concluded  that  the  gas  is  entering  into  chemical  union 
with  some  constituent  of  the  liquid.  An  instance  of  this 
will  be  quoted  later  on. 

The  definite  relationship  between  a  gas  and  an  ab- 
sorbent liquid  is  frequently  expressed  by  means  of  the 
'absorption  coefficient.'  This  is  defined  as  the  volume 


22  PHYSICAL   CHEMISTKY 

of  the  gas  (reduced  to  N.T.P.)  which  is  absorbed  by  unit 
volume  of  the  liquid  under  normal  pressure  (i.e.  1 
atmosphere).  The  statement,  for  instance,  that  the  ab- 
sorption coefficient  of  oxygen  in  water  at  20°  is  0'031, 
means  that  1  cub.  cm.  of  water  at  20°  absorbs  under  1 
atmosphere  pressure  0'031  cub.  cm.  of  oxygen  (measured 
at  N.T.P.).  The  following  table  shows  the  values  of  the 
absorption  coefficient  for  some  common  gases  in  water : — 

Temperature.  Oxygen.  Nitrogen.  Carbon  Dioxide. 

0°  -0489  O239  T713 

10"*  -0380  -0196  1-194 

20°  O310  -0164  0-878 

30°  -0262  -0138  0-665 

40°  0231  -0118  0-530 

The  figures  quoted  show  that  oxygen  is  more  soluble 
in  water  than  nitrogen,  that  carbon  dioxide  is  much  more 
soluble  than  either  oxygen  or  nitrogen,  and  that  in  all 
cases  the  solubility  diminishes  as  the  temperature  rises. 

Sometimes  the  relationship  between  a  gas  and  an  ab- 
sorbent liquid  is  expressed,  not  by  the  absorption  coeffi- 
cient, but  by  the  'solubility,'  defined  as  the  volume  of 
gas  (measured  at  t°  the  temperature  of  experiment) 
which  is  absorbed  by  unit  volume  of  the  liquid  under 
any  pressure.  If  A  represents  the  absorption  coefficient 
and  I  the  solubility,  the  relation  between  them  is  given 
by  the  equation  l  =  A(l+a£). 

Diffusion   of  a   Gas   through   a   Liquid  Film. — The 

velocity  of  diffusion  of  a  gas  through  a  very  thin  porous 
septum  is  closely  related,  as  we  have  already  seen,  to 
the  density  of  the  gas.  But  a  new  factor  has  to  be  taken 
into  account  when  we  are  dealing  with  the  passage  or 
diffusion  of  a  gas  across  a  liquid  film.  The  velocity  of 
this  diffusion  depends  on  the  power  of  the  liquid  to 
dissolve  the  gas,  and  is,  as  a  matter  of  fact,  directly  pro- 
portional to  the  absorption  coefficient  of  the  gas  in  the 


ABSORPTION   OF  GASES   BY   LIQUIDS      23 

liquid.  The  direction  of  diffusion  in  such  a  case  is  natu- 
rally from  the  side  of  the  film  where  the  pressure  of  the 
gas  is  high  to  the  side  where  it  is  low,  the  gas  being 
taken  into  solution  at  the  one  surface  and  passed  out  of 
solution  at  the  other.  Other  things  being  equal,  the 
amount  of  gas  diffusing  across  such  a  film  in  a  given 
time  will  be  proportional  to  the  difference  in  the  pressure 
of  the  gas  on  the  two  sides. 

That  the  solubility  of  a  gas  is  all-important  in  deter- 
mining the  velocity  of  its  diffusion  across  a  liquid  film" 
has  been  shown  by  Exner1  for  soap  bubbles,  and  bj^ 
Wiesner  and  Molisch 2  for  vegetable  membranes  impreg- 
nated with  water.  In  both  these  cases  carbon  dioxide, 
although  twenty-two  times  heavier  than  hydrogen,  dif- 
fuses much  more  rapidly  than  the  latter,  for  the  absorp- 
tion coefficient  of  hydrogen  is  small,  and  of  the  same 
order  of  magnitude  as  those  of  oxygen  and  nitrogen 
quoted  above.  Similarly,  carbon  dioxide  diffuses  through 
moist  vegetable  membranes  much  more  rapidly  than 
oxygen,  a  fact  which  is  of  importance  in  relation  to 
the  gas  exchange  between  the  plant  and  the  atmosphere. 
It  should  be  noted  that  the  presence  of  water  is  essential 
to  the  diffusion,  for  the  air-dried  membranes  are  almost, 
if  not  altogether,  impermeable  to  these  gases.3 

The  difference  between  an  easily  soluble  and  a  spar- 
ingly soluble  gas  in  connection  with  diffusion  across  a 
film  of  water  is  easily  demonstrated.  For  this  purpose 
the  apparatus  shown  in  Fig.  2  may  be  employed.  The 
one  end  of  a  short,  wide  tube  a  is  opened  out  slightly, 
and  a  piece  of  pig's  bladder  is  tied  over  it  and  well 
sealed.  The  other  end  is  closed  by  a  rubber  stopper 

1  Sitzungsber.  k.  AJcad.  Wiss.   Wien,  1874,  70,  ii.  465* 

2  Jbid.,  1889,  98,  i.  670. 

3  Wiesner  and  Molisch,  loc.  cit. ;  see  also  Steinbrinck,  Ber.  deutsch. 
Bot.  Gea.,  1900,  18,  275. 


24 


PHYSICAL   CHEMISTRY 


carrying  a  tube  b,  which  in  its  turn  is  connected  with 
some  arrangement  for  indicating  changes  of  pressure. 
In  the  apparatus  sketched  in  Fig.  2,  any 
increase  of  pressure  in  a  is  transmitted 
to  the  surface  of  the  coloured  liquid  in 

c,  and  the  liquid  is  forced   up  the   tube 

d.  If  now,  when  the  membrane  has  been 
impregnated  with  water  and  the  apparatus 
has  then  been  set  up,  a  beaker  is  inverted 
over  a  and  filled  with  hydrogen,  no  appre- 
ciable  movement   of    the   liquid   in   d   is 
observed.      A  positive  result,  however,  is 
obtained  when  the  hydrogen  in  the  beaker 
is  replaced  by  a  gas  which  is  very  soluble 
in  water;   with  ammonia,  for  instance,  a 
distinct   rise   of    the   liquid    in   d  is   ob- 
served in  a  very  short  time. 

The  power  of  water  to  dissolve  oxygen 
and  carbon  dioxide  is  an  all-important 
fact  in  connection  with  aquatic  plants. 
The  possibility  of  gaseous  interchange 
between  the  air  and  the  cells  of  the 
submerged  plant  depends  in  the  first  place 
on  the  diffusion  of  oxygen  and  carbon 
dioxide  through  the  medium  surrounding 
the  plant,  for  if  the  medium  is  freed 
and  kept  free  from  air  the  plant  dies. 
In  general  the  epidermis  of  the  sub- 
merged leaf  is  not  cuticularised,  and  is  un- 
provided with  stomata.  It  is,  however, 
impregnated  with  water,  and  the  exchange  of  oxygen  and 
carbon  dioxide  between  the  surrounding  medium  and  the 
interior  of  the  leaf  consists  in  a  diffusion  across  this  water- 
logged layer.  It  has  been  shown1  that  this  diffusion  across 
1  Devaux,  Ann.  Sci.  Nat.,  1889,  [vii.],  9,  35. 


FIG.  2. 


ABSOKPTION   OF  GASES   BY   LIQUIDS      25 

the  walls  of  submerged  plants  is  subject  to  the  same  laws 
as  regulate  the  passage  of  gases  across  a  film  of  water. 
The  gaseous  interchange  of  aquatic  plants  must  there- 
fore be  a  comparatively  slow  process,  but  in  the  character- 
istic development  of  intercellular  spaces  there  is  a 
mechanism  which  deals  with  this  difficulty.  By  this 
means  the  oxygen  and  carbon  dioxide  liberated  in  the 
processes  of  assimilation  and  respiration  respectively  are 
kept  available  for  future  use.  Thus  it  is  that  those 
parts  of  aquatic  plants  which  lie  in  the  mud  at  the  bottom 
are  supplied  with  oxygen  without  depending  on  the  slow 
diffusion  of  this  gas  through  the  surrounding  water.1 

Another  point  of  interest  in  connection  with  the  gas 
exchange  of  aquatic  plants  is  the  fact  that  marine 
algaB  flourish  more  luxuriantly  in  arctic  than  in  tropical 
waters.  This  is  due  to  the  greater  solubility  of  carbon 
dioxide  in  water  at  low  temperatures  and  the  resulting 
increase  in  the  facilities  for  gaseous  interchange. 

Various  investigators  regard  the  gas  exchange  which 
takes  place  through  the  walls  of  the  lungs  as  determined 
simply  by  the  principles  which  govern  the  diffusion  of 
a  gas  across  a  liquid  film.2  It  has  been  estimated  that 
the  lung  surface,  regarded  as  a  purely  physical  apparatus, 
would  allow  the  diffusion  of  about  1450  cub.  cm.  of 
oxygen  per  minute  in  the  case  of  an  adult,  and  some 
physiologists  hold,  therefore,  that  there  is  no  need  to 
assume  the  existence  of  a  special  secretive  power  in  the 
lung  membrane.  This  is  a  point,  however,  011  which 
there  appears  to  be  considerable  difference  of  opinion, 
many  physiologists  3  holding,  on  the  other  hand,  that  the 
lung  membrane  is  the  scene  of  a  special  secretive  action. 
They  maintain  that  the  pressure  of  oxygen  in  the  blood 

1  See  Goebel,  Pflanzenbiologische  Schilderungen,  ii.  252. 

2  A.  and  M.  Krogh,  Skand.  Arch.  PhysioL,  1910,  23,  179. 

3  See  Bohr,  NageVs  ffandbuch  der  Physiologic,  i.  142  ;  Douglas  and 


1QT)     44 


26  PHYSICAL  CHEMISTRY 

is,  under  certain  circumstances,  higher  than  that  in  the 
lung  cavities.  If  this  is  so,  then  the  actual  direction 
of  diffusion  is  opposed  to  that  which  the  physical  law 
demands. 

The  air-bladder  of  fishes  is  undoubtedly  a  case  in  which 
we  must  assume  a  special  secretive  activity.  By  keeping 
a  fish  alternately  at  the  surface  and  at  various  depths 
below  the  surface  it  is  possible  to  bring  about  varia- 
tions in  the  percentage  of  oxygen  in  its  air-bladder. 
This  organ  is  the  scene  of  a  secretion  of  oxygen,  and 
the  process  is  under  the  control  of  the  nervous  system.1 

Solubility  of  Gases  in  Salt  Solutions. — As  a  general 
rule,  a  gas  is  less  soluble  in  a  salt  solution  than  it  is  in 
pure  water  at  the  same  temperature,  and  the  more 
concentrated  the  salt  solution  the  greater  is  the  lower- 
ing of  the  solubility.  It  is  on  an  analogous  principle 
that  the  'salting  out'  of  organic  compounds,  sparingly 
soluble  in  water,  is  based.  The  lower  absorptive  power 
of  salt  solutions  may  be  illustrated  by  the  following 
figures  for  the  solubility  of  oxygen  at  25°  in  half -normal, 
normal,  and  twice-normal  solutions  of  sulphuric  acid 
and  sodium  chloride ;  the  solubility  of  oxygen  in  pure 
water  at  this  temperature,  it  should  be  noted,  is  0-0308: — 

|.  N.  2N. 

Sulphuric  acid  0'0288         0*0275          0-0251 

Sodium  chloride  0'0262         0'0223          0-0158 

It  is  interesting  to  contrast  with  this  the  power  of 
blood  to  absorb  oxygen.  Amongst  other  things  blood 
contains  in  solution  appreciable  quantities  of  salts,  and 
hence,  in  accordance  with  the  general  rule  just  discussed, 
one  might  expect  the  solvent  power  of  blood  for  gases 
to  be  lower  than  that  of  water  at  the  same  temperature. 

1  Bohr,  loc.  cit.,  163. 


ABSORPTION   OF  GASES   BY   LIQUIDS      27 

Now  at  15°  C.  and  150  mm.  pressure  (that  is,  the  partial 
pressure  of  oxygen  in  the  air)  100  cub.  cm.  of  water  can 
absorb  about  07  cub.  cm.  of  oxygen,  but  100  cub.  cm. 
of  dog's  blood  absorbs  under  these  conditions  about  24 
cub.  cm.  of  that  gas.  If  the  blood  is  centrifuged,  and 
the  corpuscles  are  thus  separated  from  the  plasma,  it  can 
be  shown  that  100  cub.  cm.  of  the  latter  take  up  under 
the  afore-mentioned  conditions  0*65  cub.  cm.  of  oxygen. 
The  solvent  power  of  the  plasma  is  therefore  slightly 
less  than  that  of  water,  and  it  is  evidently  the  corpuscles 
which  are  responsible  for  the  greater  absorptive  power 
of  blood  as  a  whole  compared  with  water. 

This  difference  between  the  plasma  and  the  blood  as 
a  whole  is  brought  out  also  by  a  study  of  the  way  in 
which  the  quantities  of  oxygen  dissolved  in  the  two  media 
are  affected  by  altering  the  pressure  under  which  the 
absorption  takes  place.  In  the  case  of  the  plasma  the 
quantity  of  gas  dissolved  is  proportional  to  the  pressure 
— a  behaviour  in  strict  accordance  with  Henry's  law. 
With  the  blood  as  a  whole,  on  the  other  hand,  there  is 
no  such  proportionality.  At  low  pressures  the  increase 
in  the  amount  of  gas  dissolved  for  a  given  rise  of  pressure 
is  much  greater  than  at  high  pressures ;  the  quantity  of 
oxygen  taken  up  by  the  blood  at  760  mm.  pressure  is 
not  very  much  greater  than  the  quantity  absorbed  under 
150  mm.  pressure,  although  on  the  basis  of  Henry's 
law  it  ought  to  be  about  five  times  as  great.  The  ac- 
companying figure  (Fig.  3)  will  make  clear  the  essen- 
tial difference  between  blood  and  plasma  in  relation  to 
oxygen. 

As  has  already  been  pointed  out,  deviation  from  strict 
adherence  to  Henry's  law  means  that  the  gas  is  entering 
into  combination  with  the  solvent  or  with  something 
dissolved  in  the  solvent.  So  it  is  in  this  case ;  the 
absorption  of  oxygen  by  the  blood  is  not  merely  a 


28 


PHYSICAL   CHEMISTRY 


physical  process ;  the  gas  is  chemically  fixed  by  the 
hsemoglobin  in  the  corpuscles,  and  as  the  formation  of 
the  compound  is  tolerably  complete  at  low  pressures,  the 
form  of  the  upper  curve  becomes  intelligible. 

The  absorption  of  carbon  monoxide  and  carbon  dioxide 
by  the  blood  is,  it  should  be  noted,  subject  to  similar 
influences. 

A  brief  reference  has  already  been  made  to  the  general 

Blood 


Plasma 


Oxygen   Pressure 

FIG.  3. 

rule,  that  a  gas  is  less  soluble  in  a  salt  solution  than 
in  pure  water  at  the  same  temperature.  In  addition  to 
salts,  acids,  and  bases,  however,  there  are  other  substances, 
such  as  sucrose  (cane  sugar),  which  have  a  similar  effect 
in  lowering  the  solubility  of  gases.  The  question  as  to 
the  cause  of  this  influence  has  lately  attracted  a  good 
deal  of  attention,  inasmuch  as  it  appears  to  be  closely 
related  to  the  larger  question  of  the  possible  hydration 
of  dissolved  substances,  and  therefore  also  to  the  im- 
portant problem  of  the  nature  of  solution. 

One  salient  fact  which  has  emerged  in  the  study  of 


ABSORPTION   OF  GASES   BY  LIQUIDS     29 

the  influence  of  salts  on  the  solubility  of  gases  is,  that 
the  relative  effects  of  different  salts  are  nearly  inde- 
pendent of  the  particular  gas  employed.  It  has  been 
found  that  when  a  number  of  salts  are  arranged  according 
to  the  magnitude  of  their  influence  on  the  solubility 
of  one  gas,  the  order  is  in  general  the  same  as  when  they 
are  arranged  according  to  the  magnitude  of  their  influence 
on  the  solubility  of  another  gas.  It  follows,  therefore, 
that  the  diminished  solvent  power  of  a  salt  solution  as 
compared  with  water  is  mainly  determined,  not  by  the 
specific  nature  of  the  dissolved  gas,  but  by  some  factor  which 
is  involved  in  the  relationship  of  the  water  and  the  salt. 
In  support  of  this  conclusion  a  number  of  salts,  acids, 
and  bases  are  arranged  in  the  following  table1  according 
to  the  magnitude  of  their  influence  at  the  same  concen- 
tration on  the  solubility  of  carbon  dioxide  (I.),  hydrogen 
(II.),  and  nitrous  oxide  (III.).  The  substances  are  so 
arranged  that  the  influence  increases  from  the  top  to 
the  bottom  of  the  column,  and  it  will  be  observed  ths^fc 
the  relative  positions  are  nearly  the  same  in  each  case. 

L  II.                                III. 

HN03  HN03  HNO3 

HC1  HC1  HC1 

H2S04  H2SO4  H2S04 

CsCl  LiCl  CsOl 

KNO3  KNO3  KN03 

KI  KC1  KI 

RbCl  NaN03  KBr 

KBr  NaCl  LiCl 

KC1  KOH  RbCl 

NaCl  NaN03 

KC1 
KOH 

Another    important    experimental    result    which    must 
be   kept   in  view  by   any  one  who  attempts   an   inter- 
1  See  Geffcken,  Zeit.  physical.  Chan.,  1904,  49,  284. 


30  PHYSICAL   CHEMISTKY 

pretation  of  these  phenomena  is,  that  the  influence  of 
a  given  salt  in  lowering  the  solubility  is  greatest  in 
dilute  solution.  To  extract  this  result  from  the  actual 
experimental  data,  it  is  necessary  to  deal  with  what  is 
known  as  the  '  equivalent  relative  lowering  of  the  solu- 
bility/ Suppose  that  10  is  the  solubility  of  a  gas  in 
pure  water,  and  that  I  is  its  solubility  in  a  salt  solution 
containing  n  gram  equivalents  per  litre,  then  l^  —  l  is 
the  lowering  of  solubility  and  ~ —  is  the  relative  lower- 
ing of  solubility.  As  a  glance  at  the  table  on  p.  26 

will  show,  the  value  of  —, —  increases  as  the  concentra- 

^o 
tion   of    the    salt   solution   increases.      If,    however,    we 

compare   the  values  of    -  .  ^-t  the  equivalent   relative 

n        LQ 

lowering  of  the  solubility,  that  is,  if  we  take  the 
values  of  the  relative  lowering  per  gram  equivalent 
of  salt,  there  is  a  decrease  as  the  concentration  of  the 
salt  solution  increases.  That  means,  to  take  a  special 
case,  that  the  efficiency  of  sodium  chloride  in  lower- 
ing the  solubility  of  a  gas  is  in  normal  solution  less 
than  twice  as  great  as  the  efficiency  of  this  salt  in 
semi-normal  solution.  The  following  data,  relating  to 
the  lowering  of  the  solubility  of  hydrogen  at  15°  by 
sodium  chloride  and  potassium  nitrate,  will  make  this 
point  clear ;  the  figures  in  the  table  are  the  values 

f  i  k-i 
of  •  •  ~v 

Concentration  of  Sodium  Potassium 

Salt  Solution.  Chloride.  Nitrate. 

1-0  normal  '22  -19 

2-0       „  -20  -16 

3-0       „  -18  -14 

The    fact   that    the   value   of    -  •  ^-  increases   with 

n        IQ 

dilution  is  a  result  of  the  utmost  importance,  for  it 
shows  that  the  cause  which  is  at  work  in  lowering  the 


ABSOKPTION   OF   GASES   BY   LIQUIDS      31 

solubility  is  relatively  most  potent  in  dilute  solutions. 
It  has  sometimes  been  suggested  that  the  influence  of 
salts  on  the  solubility  of  gases  is  specially  marked  in 
concentrated  solution,  but  the  experimental  evidence  is 
distinctly  opposed  to  this  view. 

Interpretations  of  the  Lowering  of  the  Solubility 
of  Gases. — It  would  be  going  beyond  the  scope  of  this 
volume  to  discuss  in  detail  the  attempts  that  have  been 
made  to  interpret  the  effect  which  salts  and  some  non- 
electrolytes  have  on  the  solubility  of  gases.  It  is,  how- 
ever, desirable  to  indicate  briefly  what  explanations  have 
been  suggested. 

First,  it  has  been  maintained  that  the  influence 
exerted  by  a  salt  is  connected  with  the  internal  pressure 
of  the  solution.  When  a  salt  is  dissolved  in  water, 
there  is  an  increase  of  the  internal  pressure,  which 
is  regarded  as  equivalent  to  a  corresponding  increase 
of  the  external  pressure.  This  would  mean  an  extra 
resistance  offered  to  any  increase  in  the  bulk  of  the 
liquid,  such  an  increase,  for  instance,  as  that  which 
results  from  the  absorption  of  a  gas.  Owing,  then, 
the  increased  resistance  to  expansion  brought  about 
by  the  salt,  less  gas  will  be  absorbed  by  a  salt  solutioi 
than  by  pure  water. 

Some  workers  who  adopt  this  first  line  of  explanation 
prefer  to  deal  with  compressibility  instead  of  internal 
pressure,  maintaining  that  the  power  of  a  liquid  to  dis- 
solve a  sparingly  soluble  gas  is  quantitatively  related 
to  its  compressibility.1  Attention  is  drawn  to  the  paral- 
lelism between  the  lowering  of  compressibility  and  the 
lowering  of  gas  solubility  which  are  the  result  of  add- 
ing salts  to  water. 

Secondly,  it  has  been  suggested  that  the  lower  solvent 

1  Ritzel,  Zeit.  pkysikal.  Chem.,  1907,  60,  319. 


•- 

32  PHYSICAL   CHEMISTRY 

power  of  a  salt  solution  as  compared  with  water  is  due 
to  the  hydration  of  the  dissolved  salt.1  Part  of  the 
water  in  a  salt  solution  is  supposed  to  be  in  com- 
bination with  the  salt,  the  solvent  which  is  thus  appro- 
priated by  the  salt  being  no  longer  free  to  absorb 
gas.  The  influence  of  some  non-electrolytes2  in  lowering 
the  solubility  of  gases  may  be  regarded  from  the  same 
point  of  view.  If  it  is  supposed  that  the  non-electrolyte 
or  electrolyte,  as  the  case  may  be,  is  not  responsible  for 
any  absorption,  then  the  solvent  powers  of  different  salt 
solutions  for  gases  can  fairly  be  compared  only  when  we 
put  side  by  side  the  figures  for  a  definite  quantity  of 
solvent  in  each  case ;  we  must  consider  the  quantity  of 
gas  absorbed,  not  by  unit  volume  of  the  solution,  but  by 
that  volume  of  solution  which  contains  unit  volume  of  the 
solvent.  For  it  must  be  borne  in  mind  that  in  many  cases 
1000  cub.  cm.  of  a  concentrated  aqueous  solution  do  not 
contain  anything  like  1000  grams  of  water.  A  litre  of  a 
10  per  cent,  sucrose  solution,  for  instance,  contains  at 
ordinary  temperatures  only  about  934  grams  of  water, 

On  the  basis  of  these  assumptions,  it  is  possible  to 
calculate  from  the  lowering  of  the  absorption  coefficient 
the  '  average  molecular  hydration '  of  a  dissolved  electro- 
lyte or  non-electrolyte,  that  is,  the  number  of  molecules 
of  water  which  on  the  average  are  attached  to  one 
molecule  of  dissolved  substance.  In  the  case  of  sucrose, 
to  take  a  special  instance,  the  average  molecular  hydration 
is  about  6,  a  figure  which  agrees  well  with  the  values 
obtained  by  other  methods.3 

1  Rothmund,  Zeit.  pliysikal.  Chem.,   1900,  33,  413;    Philip,  Trans. 
Faraday  Soc.,  1907,  3,  140. 

2  That  is,  substances  like  sucrose  or  dextrose,  the  aqueous  solutions  of 
which  do  not  conduct  the  electric  current  to  any  appreciable  extent. 

3  See  Jones  and  Getman,  Amcr.  Chcm.  Journ.,  1904,32,319  ;  Callendar, 
Proc.  Roy.  Soc.,  A,  1908,  80,  499, 


CHAPTER  III 

OSMOTIC    PRESSURE 

Diffusion  and  Osmotic  Pressure. — In  a  previous  chapter 
reference  has  been  made  to  the  diffusion  of  gases, 
to  the  tendency  they  exhibit  to  move  from  places  where 
the  concentration  is  high  to  places  where  the  concen- 
tration is  low.  Diffusion,  however,  is  a  phenomenon  which 
is  characteristic  not  only  of  gases  but  also  of  solutions, 
and  in  the  latter  case  also  is  to  be  regarded  as  a  mole- 
cular movement,  not  as  a  movement  in  mass.  If  a 
layer  of  strong  sugar  solution  is  put  at  the  bottom  of 
a  tall  cylinder,  and  water  is  carefully  added,  with  as 
little  mixing  as  possible,  a  process  of  diffusion  commences 
which  does  not  cease  until  the  sugar  concentration  is 
the  same  at  all  points  throughout  the  liquid.  The  sugar 
moves  from  places  where  its  concentration  is  high  to 
places  where  its  concentration  is  low,  although  naturally, 
owing  to  the  greater  friction,  the  rate  of  movement  is 
very  much  below  that  observed  in  gaseous  diffusion.  In 
addition  to  recognising  this  common  characteristic  of 
diffusion  we  may,  in  considering  the  analogy  between 
gases  and  dissolved  substances,  go  a  step  further,  and 
regard  the  movement  as  due  in  each  case  to  a  pressure. 
Just  as  we  speak  of  the  pressure  of  a  gas  driving  the 
molecules  from  places  of  high  concentration  to  places 
of  low  concentration,  so  we  may,  by  way  of  analogy 
at  least,  regard  the  molecules  of  a  dissolved  substance 

33  G 


34  PHYSICAL  CHEMISTEY 

as    diffusing    under    the    influence    of    a    pressure — the 
osmotic  pressure,  as  it  is  called. 

Semi-permeable  Membranes. — Gaseous  pressure  may 
be  realised  and  measured  at  some  surface  interposed  to 
prevent  further  expansion.  Similarly,  osmotic  pressure 
might  be  realised^ and  measured  at  some  surface  inter- 
posed to  prevent  further  expansion,  that  is,  diffusion,  of 
the  dissolved  substance.  If,  however,  this  surface  (some 
kind  of  membrane,  for  instance)  is  to  reveal  to  us  and 
enable  us  to  measure  the  tendency  to  expansion  of  the 
dissolved  substance  only,  then  it  must  allow  free  passage 
to  the  solvent  and  block  the  further  advance  of  the 
dissolved  substance ;  it  must  differentiate  between  solvent 
and  solute ;  it  must  be  *  semi-permeable.'  Given  that  a 
solution  is  separated  from  the  solvent  by  a  surface  or 
membrane  satisfying  these  specified  conditions,  then 
diffusion  of  the  dissolved  substance  is  impossible.  Such 
a  system,  however,  is  not  in  equilibrium,  for,  so  long  as 
no  hydrostatic  pressure  develops,  equilibrium  would  be 
reached  only  when  the  concentration  of  the  dissolved 
substance  is  the  same  on  both  sides  of  the  membrane. 
Since  diffusion  of  the  dissolved  substance  is  barred, 
the  system  seeks  to  get  into  the  condition  of  equilibrium 
in  the  only  other  way  which  is  possible,  namely,  by 
water  passing  through  the  membrane  into  the  solution. 

This,  then,  would  be  the  effect  of  interposing  a  semi- 
permeable  membrane  between  solvent  and  solution,  and 
the  next  question  that  arises  is,  Are  such  membranes 
known?  The  answer  is  in  the  affirmative,  for  certain 
membranes  have  been  discovered  which  are  readily 
permeable  to  water  and  are  found  to  be  practically 
impermeable  to  various  dissolved  substances.  There  is, 
for  instance,  the  membrane  which  is  formed  when  a 
drop  of  copper  sulphate  solution^on  the  end  of  a  narrow 


OSMOTIC   PRESSURE  35 

glass  tube,  is  introduced  into  a  solution  of  potassium 
ferrocyanide.  At  the  common  surface  of  the  two  solu- 
tions copper  ferrocyanide  is  deposited  as  a  thin  trans- 
parent skin  surrounding  the  drop  of  copper  sulphate. 
Once  the  skin  has  been  formed  the  precipitation  of 
copper  ferrocyanide  ceases,  the  solutions  on  either  side 
remaining  clear;  this  obviously  means  that  neither 
copper  sulphate  nor  potassium  ferrocyanide  can  penetrate 
a  membrane  of  copper  ferrocyanide.  This  membrane 
has  been  found  to  be  impermeable  also  to  various  other 
substances,  notably  sucrose  and  dextrose ;  it  may  there- 
fore be  described  as  semi-permeable  in  regard  to  (1) 
water  and  sucrose,  and  (2)  water  and  dextrose. 

When  an  aqueous  solution  of  sucrose,  then,  is  separated 
from  water  by  a  membrane  of  copper  ferrocyanide,  we 
may  hope  to  observe  the  passage  of  water  into  the 
solution,  which  has  already  been  described  as  an  inevit- 
able occurrence  in  such  a  system.  For  the  purpose  of 
quantitative  measurement,  and  even  for  the  purpose  of 
qualitative  demonstration,  the  easily  ruptured  membrane 
of  copper  ferrocyanide  must  be  supported  on  some  more 
or  less  rigid  framework.  It  may,  for  instance,  be  de- 
posited in  the  walls  of  a  small  porous  pot  of  unglazed 
porcelain.  The  pot  which  is  to  be  used  for  this  purpose 
must  be  well  washed,  and  its  walls  must  be  thoroughly 
impregnated  with  water.  It  is  then  filled  nearly  to  the 
top  with  a  dilute  solution  of  copper  sulphate  (2'5  grams 
per  litre),  and  allowed  to  stand  for  a  considerable  time 
in  a  dilute  solution  of  potassium  ferrocyanide  (2'1  grams 
per  litre).  Under  these  circumstances  the  salts  diffuse 
through  the  walls  of  the  pot,  meet  in  the  interior,  and 
deposit  a  film  of  copper  ferrocyanide.  When  the  for- 
mation of  the  membrane  is  complete  the  pot  is  thoroughly 
washed  and  soaked  in  water;  it  is  then  ready  for  use 
in  a  way  to  be  described  presently. 


36  PHYSICAL   CHEMISTRY 

There  is  another  method1  of  preparing  a  membrane 
of  copper  ferrocyanide  for  the  purpose  of  demonstration 
— a  method  which  is  in  some  ways  preferable  to  the 
first.  One  end  of  a  glass  tube,  50  mm.  long  and 
10  mm.  in  diameter,  is  dipped  in  20  per  cent,  gelatin,  to 
which  a  little  potassium  dichromate  solution  has  been  added. 
The  gelatin  film  which  is  thus  formed  over  the  end  of 
the  tube  becomes  insoluble  in  water  if  allowed  to  dry  in 
the  light ;  it  may  then  be  soaked  in  water  to  remove  the 
potassium  dichromate.  The  glass  tube  is  thus  closed  at 
one  end  by  a  diaphragm  of  insoluble  gelatin,  in  which  a 
semi-permeable  membrane  of  copper  ferrocyanide  may  be 
deposited.  A  solution  of  copper  sulphate  of  the  strength 
already  specified  is  put  inside  the  little  cell,  which  is 
then  immersed  in  potassium  ferrocyanide  solution.  The 
gelatin  diaphragm,  which  of  itself  is  practically  colour- 
less, soon  begins  to  assume  a  brown  colour ;  this  gradu- 
ally deepens  until  the  formation  of  the  membrane  is 
complete. 

The  vessel  carrying  the  membrane,  either  the  porous 
pot  or  the  glass  tube  with  the  gelatin  diaphragm,  is  then 
charged  with  sugar  solution,  and  a  rubber  stopper  carrying 
a  tube  of  narrow  bore  is  inserted  and  made  tight  with  a 
suitable  cement.  When  the  pot  or  glass  tube  is  immersed 
in  water,  the  level  of  the  liquid  in  the  narrow  tube  soon 
begins  to  rise  slowly,  and,  if  the  membrane  has  been  well 
made,  ultimately  attains  a  considerable  height.  If  the 
membrane  were  strong  enough,  and  no  leaks  were  sprung, 
water  would  continue  to  pass  through  the  membrane  until 
the  hydrostatic  pressure  of  the  liquid  column  balanced 
the  tendency  of  the  water  to  force  its  way  in.  In  most 
cases,  however,  where  no  special  precautions  have  been 
taken,  the  cell  breaks  down  long  before  this  condition  of 
equilibrium  has  been  reached. 

1  Tammann,  Zeit.  physical.  Chem.,  1892,  10,  700. 


OSMOTIC   PRESSURE  37 

The  Semi-permeable  Covering  of  Barley  Grains. — III 

addition  to  copper  ferrocyanide  and  other  similar  preci- 
pitation membranes,  there  are  numerous  plant  and  animal 
membranes  which  are  permeable  to  water  but  imperme- 
able to  many  dissolved  substances ;  they  are  therefore 
semi-permeable.  An  interesting  case  of  a  semi-permeable 
membrane  in  the  vegetable  world  was  described  lately 
by  Brown.1  He  has  shown  that  certain  barley  grains 
(Hordeum  vulgar e  var.  ccerulescens)  have  a  covering  which 
exhibits  selective  action  when  placed  in  aqueous  solutions 
of  sulphuric  acid  and  various  other  substances ;  water 
is  absorbed  by  the  grains,  whilst  the  dissolved  substance 
cannot  gain  an  entrance.  That  sulphuric  acid  cannot 
penetrate  the  covering  of  the  grain  is  shown  by  the 
fact  that  a  blue  pigment  which  is  present  in  the  aleurone 
cells,  and  which  is  turned  red  by  acids,  remains  unaffected 
when  undamaged  barley  grains  are  soaked  in  sulphuric 
acid.  On  the  other  hand,  any  grain  the  covering  of 
which  is  imperfect  or  has  been  purposely  perforated,  at 
once  begins  to  exhibit  the  colour  change  denoting  the 
access  of  acid  to  the  interior.  Grains  which  have  been 
exposed  to  the  action  of  boiling  water  for  thirty  minutes, 
and  which,  after  this  treatment,  have  lost  all  power  of 
germinating,  behave  in  the  same  way  as  untreated  grains, 
so  that  the  semi-permeable  character  of  the  covering 
does  not  depend  on  the  activity  of  living  protoplasm. 

A  sugar  solution  separated  from  water  by  a  membrane 
of  copper  ferrocyanide  draws  water  through  the  membrane, 
and  similarly  the  contents  of  barley  grains  steeped  in 
pure  water  attract  water  (up  to  about  70  per  cent,  of 
their  weight)  through  the  semi-permeable  covering  with 
which  they  are  surrounded.  If  it  were  possible  to  replace 
the  contents  of  a  barley  grain  by  a  solution  of  sulphuric 
acid,  then  on  steeping  in  water  the  same  phenomenon 

1  Annals  Bot  ,  1907,  21,  79;  also  Proc.  Roy.  Soc.,  B,  1909,  81,  82. 


38  PHYSICAL   CHEMISTRY 

would  be  observed  as  in  the  case  of  the  actual  barley 
grain — water  would  enter  through  the  semi-permeable  cover- 
ing. We  may  therefore  regard  the  barley  seed  contents  and 
a  solution  of  sulphuric  acid  as  both  capable  of  attracting 
water  across  a  semi-permeable  membrane,  and  hence  the 
steeping  of  barley  grains  in  a  solution  of  sulphuric  acid 
results  in  a  competition  for  water  between  the  seed  con- 
tents and  the  sulphuric  acid.  In  this  connection  the 
experiments  made  by  Brown  with  solutions  of  sodium 
chloride  are  interesting.  This  salt  resembles  sulphuric 
acid  in  being  unable  to  penetrate  the  covering  of  the 
barley  grain,  and  in  the  competition  for  water  between 
the  seed  contents  and  a  solution  of  sodium  chloride  the 
amount  of  water  which  the  former  can  attract  /depends  on 
the  concentration  of  the  salt  solution.  As  this  is  raised, 
the  barley  grains  absorb  less  and  less  water :  the  amou.nt 
absorbed  from  a  2  per  cent,  salt  solution  is  about  41  per 
cent,  of  the  weight  of  the  seeds,  while  from  a  saturated 
salt  solution  it  is  only  about  14  per  cent.  By  way  of 
contrast,  it  is  instructive  to  find  that  when  barley  grains 
are  steeped  in  a  solution  of  a  substance  which  can  pene- 
trate the  seed  covering  (e.g.  acetic  acid  or  ethyl  alcohol) 
the  amount  of  water  absorbed  is  nearly  the  same  as  when 
they  are  steeped  in  pure  water.  There  is  in  this  case  no 
competition  for  the  water. 

Another  illustration  of  the  comparative  impermeability 
of  seed  coverings  to  certain  substances  is  found  in  the 
use  of  copper  sulphate  as  a  fungicide.  This  salt  is  highly 
poisonous  for  the  vegetable  organism,  and  yet  it  is  possible 
to  steep  wheat  in  a  solution  of  copper  sulphate  and  so 
destroy  any  adherent  fungus  spores  without  affecting  the 
vitality  of  the  seed  itself. 

Pf offer's  Work  on  Osmotic  Pressure. — At  the  begin- 
ning of  this  chapter  osmotic  pressure  has  been  referred 
to  as  the  driving  force  under  the  influence  of  which  the 


OSMOTIC  PEESSURB  39 

molecules  of  a  dissolved  substance  diffuse.  With  the 
interposition  of  a  semi-permeable  membrane  between  sol- 
vent and  solution,  diffusion  of  the  solute  becomes  im- 
possible, and  the  corresponding  reverse  movement  of 
solvent  into  solution  is  observed.  The  driving  force  be- 
hind this  movement  is  opposite  in  direction  to  the  osmotic 
pressure,  but  is  equivalent  to  it.  Hence  if  we  can  measure 
the  tendency  of  water  to  pass  into  a  solution  through  a 
semi-permeable  membrane,  if,  in  other  words,  we  can 
measure  the  force  of  the  attraction  between  solvent  and 
solution,  we  are  at  the  same  time  determining  the  osmotic 
pressure  of  the  solution. 

There  are  various  conceptions  current  with  regard  to 
the  nature  of  osmotic  pressure.  Some  regard  it  as  being 
of  kinetic__origin,  strictly  comparable  with  the  pressure 
exerted  by  a  gas  on  the  walls  of  the  containing  vessel ; 
others  consider  it  simply  as  the  expression  of  the  attrac- 
tion between  solvent  and  solution;  and  others  still  believe 
it  to  be  closely  related  to  surface  tension.  But  whatever 
views  may  be  held  as  to  the  nature  of  osmotic  pressure, 
there  is  no  doubt  that  what  is  determined  in  actual 
measurement  is  the  force  with  which  the  solvent  seeks 
to  enter  the  solution  through  a  semi-permeable  membrane. 

The  pioneer  work  in  the  direct  measurement  of  osmotic 
pressure  was  carried  out  in  the  seventies  of  last  century 
by  Pfeffer,  then  professor  of  botany  in  Basle.  His  ex- 
perimental results  form  part  of  the  foundation  on  which 
the  modern  theory  of  solution  rests,  and  demand  therefore 
at  least  a  brief  consideration. 

Pfeffer  measured  the  pressure  developed  in  an  osmotic  cell 
which  was  charged  with  a  solution  and  immersed  in  water. 
The  osmotic  cell  consisted  of  a  small  porous  pot  with  a 
semi-permeable  membrane  of  copper  f errocyanide  deposited 
close  to  the  inner  surface.  By  means  of  various  connecting 
pieces  the  pot  communicated  with  a  closed  manometer 


40 


PHYSICAL  CHEMISTRY 


which  served  to  register  the  pressure.  The  relation  of 
these  various  parts  will  be  clear  from  Fig.  4.  The 
necessity  for  using  a  closed  manometer  instead  of 
an  open  one  will  be  apparent  when  it  is  pointed  out 
that  with  an  open  manometer  so  much  water  would 
enter  the  cell  that  the  concentration  of  the  solution 
would  be  materially  altered.  The  pressure  measured 
in  an  open  manometer,  except  for  a  very  dilute  solu- 
tion, would  be  quite  different  from  the  osmotic 
pressure  of  the  solution  put  into  the  cell.  With 
a  closed  manometer,  on  the  other  hand,  the  en- 
trance of  a  trace  of  water  develops  such  a  pressure 

in  the  cell  as  prevents  any 
more  coming  in.  Pfeffer 
estimated  that  in  a  cell 
actually  used  by  him,  and 
capable  of  holding  16  cub. 
cm.,  the  amount  of  water 
that  entered  the  cell  while 
pressure  equilibrium  was 
being  attained  was  not 
more  than  0*14  cub.  cm. 
In  all  his  experiments, 
moreover,  the  specific 
gravity  of  the  contents  of 
the  cell  was  determined 
before  and  after  the  mea- 
surement of  the  pressure, 
so  that,  if  necessary,  allow- 
ance could  be  made  for 
change  in  concentration. 

With  the  apparatus  just 
described  Pfeffer  measured 
-  4.  the  ^osmotic    pressure    of 

numerous  solutions.     Evidence  of  the  different   osmotic 


OSMOTIC   PRESSURE  41 

power  of  different  substances  is  found  in  his  figures  for 
the  osmotic  pressure  of  1  per  cent,  solutions  of  sucrose, 
potassium  nitrate,  and  potassium  sulphate,  the  values  being 
53'5,  178'0,  and  193'0  cm.  of  mercury  respectively. 

It  was  found  also  that  the  osmotic  pressure  exerted  by 
a  given  substance  in  solution  increased  with  the  concen- 
tration, as  shown  for  sucrose  in  the  first  two  columns 
of  the  following  table.  The  concentration  (c)  is  stated 
as  percentage  of  sucrose,  and  the  osmotic  pressure  (P)  is 
given  in  cm.  of  mercury.  The  figures  in  the  third  column 

are  the  values  of  the  ratio  — presfl    *—  ,  and  inspection 

concentration 

shows  that  they  are  approximately  constant. 

p.  £ . 

1  53-5  53-5 

2  101-6  50-8 
2-74  151-8  55-4 
4  208-2  52-1 
6  307-5  51-3 

The  experimental  difficulties  encountered  in  the  direct 
determination  of  osmotic  pressure  are  very  great,  and  if 
we  ascribe  to  these  the  variation  from  constancy  of  the 
figures  in  the  third  column,  we  may  conclude  that  the 
osmotic  pressure  of  a  solution  is  proportional  to  the 
concentration  of  the  dissolved  substance.  Since  the  con- 
centration of  a  given  quantity  of  dissolved  substance  is 
inversely  as  the  volume  which  the  solution  occupies,  the 
foregoing  proposition  may  be  stated  also  in  the  following 
way :  VThe  osmotic  pressure  exerted  by  a  given  quantity  of 
dissolved  substance  is  inversely  proportional  to  the  volume 
of  the  solution.  (  It  will  be  observed  that  this  very  closely 
resembles  Boyle's  law. 

Pfeffer  studied  also  the  influence  of  temperature  on 
the  osmotic  pressure  of  a  given  solution,  and  showed  that 
the  pressure  increases  as  the  temperature  rises.  His 


42  PHYSICAL  CHEMISTRY 

results  for  a  1  per  cent,  solution  of  sucrose  are  shown 
in  the  first  and  second  columns  of  the  accompanying 
table.  The  figures  in  the  third  column  are  those  cal- 

Osmotic  Pressure  in  Atmospheres. 

f  C.  Observed.  Calculated. 

6-8  0-664  0-665 

137  0-691  0-681 

15-5  0-684  0-686 

22-0  0-721  0-701 

32-0  0-716  0*725 

36-0  0-746  0-735 

culated  by  the  formula  P=P0(l+at),  where  P0  =  0*649 
and  a=2"T3 — calculated,  that  is,  on  the  assumption  that 
the  osmotic  pressure  of  a  given  solution  is  proportional 
to  the  absolute  temperature. 

The  agreement  between  the  observed  and  the  calculated 
figures  is  far  from  perfect,  but  the  differences  are  ir- 
regular, sometimes  positive,  sometimes  negative.  In  view 
of  this  and  of  the  afore-mentioned  experimental  diffi- 
culties, we  may  with  reservation  assent  to  the  proposition 
that  the  osmotic  pressure  of  a  given  solution  is  pro- 
portional to  the  absolute  temperature — a  proposition 
closely  corresponding  with  the  statement  of  Gay-Lussac's 
law  for  gases. 

Theoretical  Value  of  the  Osmotic  Pressure. — Much 
of  the  interest  attaching  to  the  subject  of  osmotic  pressure 
is  due  to  the  remarkable  parallelism  between  the  pro- 
perties of  gases  and  those  of  dissolved  substances — a 
parallelism  which  is  revealed  in  Pfeffer's  experimental 
data,  and  which  was  emphasised  by  van't  Hoff  in  1887. 
By  a  therm odynamical  argument,1  based  on  the  validity 
of  Henry's  law,  this  chemist  reached  the  conclusion  that 
the  osmotic  pressure  of  a  dilute  solution  must  be  pro- 
portional (1)  to  the  concentration  of  the  solute,  and  (2)  to 

1  Phil.  Mag.,  1883,26,81. 


OSMOTIC   PKESSURB  43 

the  absolute  temperature.  When  these  propositions  were 
advanced  the  experimental  material  available  for  their 
verification  was  very  scanty,  and  was,  in  fact,  derived 
almost  exclusively  from  Pfeffer's  measurements.  Never- 
theless, van't  Hoff  was  satisfied  that  his  theoretical 
conclusions  were  amply  verified,  and  that  he  was  justified 
in  extending  Boyle's  law  and  Gay-Lussac's  law  to  solutions. 

Moreover,  a  further  step  was  taken  in  the  extension 
of  Avogadro's  hypothesis  to  solutions,  and  van't  Hoff 
assumed  that  at  a  given  temperature  equal  volumes  of 
two  dilute  solutions  which  have  equal  osmotic  pressures 
contain  the  same  number  of  dissolved  molecules.  If 
this  assumption  is  adopted  as  a  working  hypothesis,  then 
it  follows  that  the  behaviour  of  substances  in  dilute 
solution  must  be  governed  by  an  equation  PV—RfT, 
exactly  analogous  to  the  gas  equation  pv  =  RT.  In  the 
equation  P  F=  R'T,  P  is  the  osmotic  pressure,  F  is  the 
volume  of  solution  which  contains  1  gram-molecule  of 
solute,  T  is  the  absolute  temperature,  and  R'  is  a  constant 
for  all  dissolved  substances. 

The  gas  constant  R  has  already  been  evaluated  and 
found  to  be  0*082   when  the   pressure   is   measured   in 
atmospheres  and  the  volume  in  litres.     Suppose  now  that 
we  find  the  value  of  R',  using  Pfeffer's  data.     According 
to  these,  the  osmotic  pressure  of  a   1  per  cent,  sucrose  *\ 
solution    at   0°    C.    is    0*649    of   an    atmosphere;    hence   / 
P  =  0-649    and    ?T=273.     Since  we  are  dealing   with   a 
1  per  cent,  solution  we  may,  with  close  approximation   I 
to   the   truth,    regard    100   cub.    cm.   of  the  solution  as   / 
containing  1  gram  of  sucrose  ;   F,  the  volume  of  solution   V 
which  contains  1  gram-molecule  of  sucrose,  that  is,  342    \ 
grams,   would   then  be    34200  cub.   cm.,   or  34'2  litres.    -* 


It  follows  that  #  =       =-—  =  0-0813,  a  value  very 
nearly  equal  to  that  of  R,  the  gas  constant.     It  appears 


44  PHYSICAL   CHEMISTRY 

therefore  that  Rf  =  R,  and  that  we  may  employ  the  same 
equation  to  represent  the  behaviour  of  dissolved  sub- 
stances as  is  used  in  the  case  of  gases,  except  that  what 
is  gas  pressure  in  the  one  case  is  osmotic  pressure  in  the 
other,  and  that  what  is  the  volume  occupied  by  1  gram- 
molecule  of  gas  in  the  one  case  becomes  in  the  other  the 
volume  of  solution  which  contains  1  gram-molecule  of  solute. 
As  was  pointed  out  by  van't  Hoff,  the  equality  of 
Rf  and  R  leads  directly  to  a  conclusion  of  the  utmost 
importance,  namely,  that  the  osmotic  pressure  of  a  dilute 
sugar  solution  is  equal  to  the  pressure  which  the  sugar 
would  exert  if  it  were  in  the  gaseous  state  at  the  same 
temperature,  and  occupied  the  same  volume  as  the  solution. 
Two  remarks  may  be  made  in  reference  to  this  pro- 
position. Firstly,  validity  is  claimed  for  it  only  in 
connection  with  dilute  solutions.  Van't  Hoff  himself 
applied  his  argument  to  'ideal'  solutions  only,  that  is, 
solutions  so  dilute  that  the  mutual  action  of  the  dissolved 
molecules  and  their  actual  volume  compared  with  that 
of  the  space  they  inhabit  are  negligibly  small.  Secondly, 
it  does  not  follow  from  van't  Hoff's  proposition  that 
osmotic  pressure  and  gaseous  pressure  must  be  due  to 
the  same  cause ;  the  origin  of  osmotic  pressure  may 
be  something  quite  different  from  the  molecular  impacts 
with  which,  according  to  the  kinetic  theory,  the  pressure 
of  a  gas  is  associated.  Reference  has  already  been  made 
(p.  39)  to  the  various  current  views  of  the  origin  of 
osmotic  pressure,  but  it  ought  to  be  borne  in  mind 
that  the  quantitative  relation  between  the  osmotic 
pressure,  temperature,  and  concentration  of  a  dilute 
solution  is  independent  of  the  particular  view  which 
may  be  held  in  regard  to  the  origin  of  osmotic  effects. 
In  this  connection  Larmor's  views  *  are  noteworthy.  He 
supposes  that  'each  molecule  of  tk§  dissolved  substance 

1  Nature,  1897,  55,  545. 


OSMOTIC  PEESSUKE  45 

sensibly  influences  the  molecules  around  it  so  as  to 
form  a  loosely-connected  complex,  in  the  sense,  not  of 
chemical  union,  but  of  physical  influence.  Provided  the 
solution  is  so  dilute  that  each  such  complex  is  out  of 
range  of  the  influence  of  the  other  complexes,  then  the 
principles  of  thermodynamics  necessitate  the  osmotic 
laws.  It  does  not  matter  whether  the  nucleus  of  the 
complex  is  a  single  molecule,  or  a  group  of  molecules, 
or  the  entity  that  is  called  an  ion;  the  pressure  pheno- 
mena are  determined  merely  by  the  number  of  complexes 
per  unit  volume.' 

Just  as  the  acceptance  of  Avogadro's  hypothesis  leads 
to  a  relationship  between  molecular  weight  and  density, 
and  therefore  to  a  method  of  determining  the  molecular 
weight  of  gases,  so  the  extension  of  that  hypothesis 
to  solutions  may  be  shown  to  have  a  similar  result  for 
dissolved  substances.  The  connection  between  the 
equation  PV—ET^  in  which  the  hypothesis  is  incor- 
porated, and  the  determination  of  molecular  weight  is 
easily  traced.  For,  supposing  that  a  solution  of  a  sub- 
stance containing  g  grams  per  litre  is  found  to  have  the 
osmotic  pressure  P  at  the  absolute  temperature  T,  a 
simple  calculation  gives  the  value  of  M,  the  molecular 
weight  of  the  substance.  It  must  be  remembered  that 
V  is  the  volume  of  solution  containing  1  gram-molecule 

of   solute:    we   have   therefore    V=—,    and    P^=RT. 

9  9 

Since  P,  g,  -R,  and  T  are  known,  M  can  be  calculated. 

The  determination  of  osmotic  pressure,  however,  is  not 
a  practical  method  for  ascertaining  the  molecular  weight 
of  a  dissolved  substance,  because  of  the  experimental 
difficulties  to  which  reference  has  already  been  made,  and 
which,  as  experience  has  shown,  are  solved  only  after 
much  patient  labour.  There  are  other  and  simpler 
methods  for  'determining  the  molecular  weight  of  dis- 


46  PHYSICAL  CHEMISTRY 

solved  substances,  .methods  based  on  certain  properties 
of  solutions  that  are  intimately  related  to  osmotic  pres- 
sure. These  will  be  discussed  later. 

Recent  Work  on  the  Direct  Determination  of 
Osmotic  Pressure. — At  the  time  when  van't  Hoff's 
theory  of  osmotic  pressure  was  brought  forward,  the  ex- 
perimental material  available  for  its  verification  was  ex- 
ceedingly scanty.  Indeed,  it  is  only  within  recent  years 
that  serious  and  sustained  efforts  have  been  made  to 
confirm  and  extend  Pfeffer's  work  on  the  direct  measure- 
ment of  osmotic  pressure.  The  result  of  these  efforts  has 
been  to  throw  much  light  on  the  relation  of  osmotic 
pressure  to  gas  pressure. 

Morse,  Frazer,  and  others,  in  a  lengthy  investigation,1 
have  determined  the  osmotic  pressures  of  sucrose  and 
dextrose  solutions  of  various  concentrations  and  at 
various  temperatures.  The  method  employed  is  practi- 
cally the  same  as  that  used  by  Pfeffer,  but  the  quality 
of  the  membranes  and  the  manipulation  of  the  apparatus 
have  been  so  improved  that  pressures  up  to  and  over 
20  atmospheres  are  regularly  recorded  with  great  ac- 
curacy. The  uncertainties  of  the  measurements  are,  it 
is  estimated,  confined  to  the  second  decimal  place  of  the 
figures  expressing  the  osmotic  pressure  in  atmospheres. 

The  copper  ferrocyanide  membranes  are  deposited 
electrolytically.  The  porous  pot,  thoroughly  impregnated 
with  water,  is  filled  with  potassium  ferrocyanide  solution, 
and  placed  in  copper  sulphate  solution ;  a  current  is  then 
passed  from  a  copper  electrode  in  the  copper  sulphate 
to  a  platinum  wire  in  the  ferrocyanide.  The  copper 
ferrocyanide  is  thus  deposited  in  the  walls  of  the  pot, 

1  See  Amer.  Chem.  Journ.,  1905,  34,  1  ;  1906,  36,  1,  39 ;  1907,  37,  324, 
425,  558  ;  38,  175;  1908,  39,  667;  40,  1,  194;  1909,  41,  1,  257;  1911, 
45,  91,  237,  383,  517,  554 ;  1912,  48,  29.  See  also  Professor  Findlay's 
monograph  on  Osmotic  Pressure. 


OSMOTIC   PRESSURE  47 

the  current  being  continued  until  the  electrical  resistance 
has  reached  a  maximum.  The  cell  is  then  rinsed  out 
and  soaked  in  water  for  several  hours.  This  is  followed 
by  repeated  electrolytic  treatment  until  the  resistance 
ceases  to  increase.  'The  cell  is  now  filled  with  a  sucrose 
solution,  placed  in  water,  and  allowed  to  develop  pressure. 
When  the  maximum  pressure  has  been  reached  the  cell 
is  taken  down,  rinsed,  soaked  in  water,  and  again  sub- 
jected to  the  membrane-forming  process.  The  development 
of  pressure  discovers  the  weak  places  in  the  membrane, 
and  these  are  subsequently  mended  by  the  electrolytic 
treatment.  By  repetition  of  these  two  operations  the 
membrane  ultimately  reaches  a  maximum  of  resistance 
beyond  which  it  cannot  be  forced,  and  the  cell  gives 
normal  maximum  osmotic  pressures  with  sucrose  solutions. 
The  membranes  prepared  in  this  way  are  perfectly  im- 
permeable to  sucrose,  even  in  contact  with  a  solution 
containing  1  gram-molecule  in  1000  grams  of  water. 

Besides  effecting  this  improvement  in  the  quality  of 
the  membrane,  Morse  and  his  co-workers  have  perfected 
(1)  the  connection  between  cell  and  manometer,  (2)  the 
means  of  accurately  measuring  the  pressure.  A  descrip- 
tion of  these  details,  however,  lies  beyond  the  scope  of 
this  volume. 

In  considering  the  results  of  this  recent  work  on 
osmotic  pressure,  we  may  inquire  how  far  they  show 
that  osmotic  pressure  is  proportional  to  the  concentration 
and  to  the  absolute  temperature,  how  far  also  they  bear 
out  the  contention  that  osmotic  pressure  and  gas  pressure 
are  equal.  In  regard  to  the  first  point,  it  has  been  found 
that  the  osmotic  pressure  of  a  sucrose  or  dextrose  solution 
is  proportional  to  the  concentration,  provided  the  concen- 
tration is  referred,  not  to  unit  volume  of  the  solution,  but  to 
unit  volume  of  the  solvent.  In  the  actual  work,  solutions 
were  made  up  containing  from  O'l  up  to  I'O  gram- 


48  PHYSICAL   CHEMISTRY 

molecule  of  sugar  dissolved  in  each  case  in  1000  grama 
of  water  ;  these  are  described  as  weight-normal  solutions, 
in  contrast  with  the  volume-normal  solutions  made  by 
dissolving  O'l  or  some  other  fraction  of  a  gram-  molecule 
in  water  and  making  the  solution  up  to  1  litre. 

The  following  table  will  show  that  the  osmotic  pressure 
is  proportional  to  the  concentration  as  just  defined;  the 
figures  are  those  for  dextrose  solutions  at  10°  C.  :  — 

Concentration  in  gram-molecules.  Osmotic  Pressure. 

Per  1000  gm.  of  Per  litre  of  In  Relatively  to  the 

Water.  Solution.  Atmospheres.        first  taken  as  Unity. 

0-1  0-099  2-39  1-00 

0-2  0-196  4-76  1-99 

0-5  0-474          /i  11-91  4-98 

1-0  O&ef-^  23-80  9'96 


It  is  obvious  that  the  pressures  for  the  four  solutions 
increase  in  a  ratio  which  is  very  nearly  that  of  the  con- 
centrations as  given  in  the  first  column,  but  diverges 
widely  from  the  ratio  of  the  concentrations  when  these 
are  stated  in  gram-molecules  per  litre  of  solution. 

As  regards  the  applicability  of  Gay-Lussac's  law  to 
solutions,  Morse  and  his  fellow-workers  conclude  from 
their  numerous  experiments  between  0°  and  25°  that 
the  temperature  coefficients  of  osmotic  pressure  and  gas 
pressure  are  practically  equal.  They  find,  for  instance, 
that  the  osmotic  pressure  of  a  1*0  weight-normal  solution 
of  sucrose  is  25*06  atmospheres  at  10°,  and  26;33  atmos- 
pheres at  25°.  If  the  temperature  coefficients  of 
osmotic  pressure  and  gas  pressure  were  equal,  the 
osmotic  pressure  at  25°,  calculated  from  that  at  10°, 

ought    to    be    25°283298  =  26'38    atmospheres,    in    good 

agreement  with  the  value  actually  recorded. 

The  results  obtained  by  Morse  and  his  fellow-workers 
are  of  great  interest  also  in  relation  to  van't  Hoff's 
proposition,  that  the  osmotic  pressure  of  a  dilute  sugar 


OSMOTIC   PRESSURE  49 

solution  is  equal  to  the  pressure  which  the  sugar  would 
exert  if  it  were  in  the  gaseous  state  at  the  same  tem- 
perature and  occupied  the  same  volume  as  the  solution. 
The  bearing  of  the  newer  experimental  data  on  this 
proposition  will  be  best  appreciated  by  a  study  of  the 
following  table.  It  refers  to  the  osmotic  pressures  of 
sucrose  solutions  at  15°,  and  allows  a  comparison  of  the 
observed  osmotic  pressures  with  the  values  of  the  gas 
pressure  calculated  (I.)  on  the  supposition  that  the 
gasified  substance  occupies  the  same  volume  as  the 
solution,  (II.)  on  the  supposition  that  it  occupies  the 
same  volume  as  the  solvent  in  the  solution. 

Gram-molecules  of  Sucrose.  Osmotic  Pressure  in  Atmospheres. 


1000  gm. 
Water. 

Per  litre  of 
Solution. 

Observed. 

Calc.  I. 

Calc.  II. 

o-i 

0-098 

2-48 

2-30 

2-35 

0-2 

0-192 

4-91 

4-51 

4-70 

0-4 

0-369 

9-78 

8-67 

9-40 

0-6 

0-533 

14-86 

12-51 

14-09 

0-8 

0-684 

•20-07 

16-07 

18-79 

1-0 

0-825 

25-40 

19-38 

23-49 

The  values  recorded  in  the  last  column  are  much 
closer  to  the  experimental  figures  than  the  values 
under  calc.  I.,  and  it  follows,  therefore,  at  least  for 
sucrose  solutions  at  15°,  that  the  osmotic  pressure  is 
approximately  equal  to  that  which  the  sucrose  would 
exert  if  it  were  gasified  at  the  same  temperature,  and 
the  volume  of  the  gas  were  reduced  to  that  of  the 
solvent  in  the  pure  state.  Similarly,  for  sucrose  solu- 
tions at  other  temperatures  between  0°  and  25°  the 
observed  osmotic  pressure  is  somewhat  greater  (6-11 
per  cent.)  than  the  gas  pressure  at  the  same  temperature 
calculated  on  basis  II. 

The  results,  then,  of  Morse  and  Frazer's  work  show 
that  Boyle's  law  is  approximately  applicable  to  solutions 
of  sucrose  and  dextrose  up  to  weight-normal  strength, 


50  PHYSICAL  CHEMISTRY 

provided  the  concentration  is  referred  not  to  1  litre  of 
solution,  but  to  1000  grams  of  solvent ;  it  has  been  further 
shown  that  from  0°  to  25°  Gay-Lussac's  law  applies  to 
solutions,  that  is,  the  temperature  coefficients  of  osmotic 
pressure  and  gas  pressure  are  equal.  The  theoretical 
equality  between  gas  pressure  and  osmotic  pressure 
is  not  strictly  confirmed  in  the  cases  investigated.  The 
excess  of  osmotic  pressure  over  gas  pressure  may  be 
due  to  hydration  of  the  dissolved  substance,  but  the 
question  cannot  yet  be  regarded  as  settled. 

The  osmotic  pressures  of  concentrated  solutions  of 
sucrose  and  dextrose  have  formed  the  subject  of  recent 
investigation  also  by  Lord  Berkeley  and  Mr.  Hartley.1 
Except  in  one  or  two  instances,  the  solutions  examined 
by  these  investigators  were  still  more  concentrated  than 
those  which  Morse  and  Frazer  studied.  They  have  also 
employed  another  method  of  determining  the  pressure 
which  is  required  to  hold  in  check  the  tendency  of 
water  to  enter  the  solution  through  a  semi-permeable 
membrane.  In  Lord  Berkeley's  experiments  the  copper 
ferrocyanide  membrane  is  deposited  as  near  as  possible 
to  the  outside  surface  of  a  porous  porcelain  tube  15 
cm.  long,  2  cm.  external  and  1'2  cm.  internal  diameter. 
The  means  adopted  to  produce  a  satisfactory  membrane 
are  very  similar  to  those  employed  by  Morse  and  his 
fellow- workers.  The  tube  carrying  the  membrane  fits 
axially  into  a  gun-metal  vessel  which  holds  the  solution 
(about  250  cub.  cm.) ;  by  various  devices  an  absolutely 
tight  joiat  is  secured  between  the  gun-metal  vessel 
and  the  tube,  the  open  ends  of  which  are  exposed. 
When  a  determination  of  osmotic  pressure  is  to  be 
made,  a.  rubber  stopper  carrying  a  capillary  tube  bent 
at  right  angles  is  inserted  into  each  end  of  the  porcelain 
tube ;  water  is  then  introduced  so  as  to  fill  the  porcelain 
%  Phil.  Trans.,  A,  190(7. '206,  48*. 


OSMOTIC  PEESSUEE  51 

tube  completely,  and  the  vertical  capillary  tubes  up  to 
a  certain  level.  The  gun-metal  vessel  surrounding  the 
porcelain  tube  is  now  filled  up  with  the  solution,  and 
immediately  connected  with  an  apparatus  by  means  of 
which  a  measured  hydrostatic  pressure  can  be  applied. 
It  is  obvious  that  if  this  connection  were  not  made  and 
the  solution  were  left  in  contact  merely  with  the  atmos- 
phere, water  would  pass  from  the  porcelain  tube  through 
the  membrane  into  the  solution ;  this  would  be  accom- 
panied by  a  fall  of  the  water  in  the  capillary  tube.1  In 
actual  work,  however,  as  soon  as  the  gun-metal  vessel  is 
full  it  is  connected  with  the  afore-mentioned  apparatus ; 
by  means  of  it  pressure  is  applied  to  the  solution,  and 
so  adjusted  that  water  is  prevented  from  entering.  If 
the  applied  pressure  is  too  great,  water  is  squeezed  out 
of  the  solution,  and  this  is  indicated  by  a  rise  of  the 
water  in  the  capillary  tube.  When  the  apparatus  is 
so  adjusted  that  the  water  in  the  capillary  tube  remains 
at  a  constant  level,  the  registered  pressure  is  the  equili- 
brium pressure  of  the  solution  for  a  pressure  of  1 
atmosphere  on  the  solvent. 

In  this  way  Lord  Berkeley  and  Mr.  Hartley  have 
obtained  the  following  values  for  the  osmotic  pressures 
of  sucrose  and  dextrose  solutions  at  0°  C. : — 

Sucrose.  Dextrose. 

Grams  Sucrose         Osmotic  Pressure         Grams  Dextrose       Osmotic  Pressure 
per  litre  of  Solution,     in  Atmospheres.       per  litre  of  Solution,    in  Atmospheres. 

180-1  13-95  99-8  13'21 

300-2  26-77  199-5  29'17 

420-3  43-97  319'2  53'19 

540-4  67-51  448-6  87'87 

660-5  100-78  548-6  121-18 

750-6  133-74 

One  of  the  most  remarkable  things  about  these  figures 
is  the  mere  magnitude  of  the  pressures  which  have  been 

1  Only  one  of  the  capillary  tubes  is  used  for  observation ;  the  other 
is  closed  by  a  glass  stopcock. 


52  PHYSICAL  CHEMISTRY 

realised  and  measured.  It  is  indeed  a  striking  result 
that  copper  ferrocyanide  membranes  have  been  so  pre- 
pared as  to  withstand  a  pressure  of  100  atmospheres  and 
over.  Even  in  the  cases  where  the  pressure  applied  to 
the  solution  was  up  to  this  high  figure,  only  the  merest 
trace  of  sugar  as  a  rule  leaked  through  the  membrane. 

A  cursory  glance  at  the  foregoing  tables  will  show  that 
there  is  no  proportionality  between  osmotic  pressure  and 
concentration,  so  long,  at  any  rate,  as  concentration  is 
referred  to  unit  volume  of  the  solution.  It  is  easily  seen 
from  a  comparison,  for  instance,  of  the  figures  for  the 
first  and  fourth  sucrose  solutions  and  for  the  first  and 
second  dextrose  solutions,  that  the  pressure  increases 
much  more  rapidly  than  the  concentration. 

Even  when  the  concentration  is  referred  to  1  litre 
of  the  solyent,  as  was  done  by  Morse  and  his  fellow- 
workers,  the  osmotic  pressure  still  increases  more  rapidly 
than  the  concentration.  These  relationships  are  best 
brought  out  by  a  diagram,  in  which  the  osmotic  pressure 
of  sucrose  solutions  is  plotted  against  the  concentration 
(Fig.  5).  Curve  I.  represents  the  actual  data  recorded 
by  Lord  Berkeley  and  Mr.  Hartley;  curve  II.  is  a 
straight  line,  traced  on  the  assumption  that  the  osmotic 
pressure  may  be  calculated  by  the  equation  PV—ET, 
where  V  is  the  volume  of  solution  containing  1  gram- 
molecule  of  sucrose ;  curve  III.  is  traced  on  the  assumption 
that  the  osmotic  pressure  may  be  calculated  by  the  equa- 
tion PV=RT,  in  which  Fis  the  volume  of  solvent  which 
goes  to  1  gram-molecule  of  sucrose.  The  observed  os- 
motic pressure  is,  it  will  be  seen,  always  greater  than 
the  calculated  pressure,  even  when  the  latter  figure  has 
been  obtained  by  reducing  the  volume  to  that  of  the 
solvent  present.  It  is,  however,  obvious  that  as  the  solu- 
tions become  dilute  the  observed,  and  calculated  values 
approximate  more  and  more  closely  to  each  other. 


OSMOTIC   PRESSUKE 


53 


The  abnormally  high  values  recorded  by  Lord  Berkeley 
and  Mr.  Hartley  for  the  osmotic  pressures  of  sucrose  and 
dextrose  solutions  have  been  discussed  by  Callendar,1 
who  finds  that  the  discrepancy  between  observed  and 
calculated  values  disappears  when  it  is  assumed  that 
the  dissolved  substance  is  hydrated.  The  theory  which 
he  develops  leads  him  to  conclude  that  in  concentrated 


so 


620 


in 


•ii 


100  200  300  400  500  600 

Grains  sucrose  per  litre  of  Solution 

FIG.  5. 


700 


sucrose  solutions,  such  as  those  employed  by  Lord  Berkeley 
and  Mr.  Hartley,  each  molecule  of  sucrose  has  attached  to 
it  on  the  average  five  water  molecules.  This  figure  is  in 
good  agreement  with  the  value  for  the  average  molecular 
hydration  of  sucrose  deduced  from  the  influence  of  this 
substance  on  the  solvent  power  of  water  for  gases  (see 
p.  32). 

1  Proc.  Bay.  Soc.,  A,  1908,  80,  466. 


CHAPTER  IV 

THE    COMPARISON    OF    OSMOTIC    PRESSURES. 
ISOTONIC    SOLUTIONS 

Water  Exchange  between  Two  Solutions  of  Unequal 
Osmotic  Pressure. — Although  the  direct  determination  of 
osmotic  pressure  is  no  easy  matter,  there  are  several 
methods  available  for  the  comparison  of  the  osmotic  pres- 
sures of  different  solutions.  These  methods  depend  on 
the  exchange  of  water  which  takes  place  across  a  semi- 
permeable  membrane  separating  two  solutions.  For  two 
solutions  of  different  osmotic  pressure,  separated  by  a 
semi-permeable  membrane,  are  no  more  in  equilibrium 
than  solvent  and  solution  in  the  same  circumstances.  The 
osmotic  exchange  of  water  will  always  be  such  as  to 
equalise  the  pressures  on  the  two  sides  of  the  membrane ; 
the  water,  that  is,  will  pass  from  the  solution  with  smaller 
osmotic  pressure  to  the  solution  which  has  the  greater 
osmotic  pressure. 

A  simple  experiment  which  demonstrates  the  existence 
of  this  water  transport  can  be  made  with  copper  sulphate 
and  potassium  ferrocyanide  solutions.  A  tall  glass  jar 
is  filled  with  copper  sulphate  solution  of  medium  strength 
— say  1  gram-molecule  per  litre.  A  little  potassium 
ferrocyanide  solution  (nearly  saturated)  is  slowly  run  out 
from  a  narrow  glass  tube,  the  end  of  which  dips  below 
the  surface  of  the  copper  sulphate  solution.  As  the 
potassium  ferrocyanide  runs  out  a  transparent  membrane 
of  copper  ferrocyanide  is  formed  where  the  solutions 

64 


COMPAKISON  OF  OSMOTIC   PRESSUKES     55 

meet.  A  bag  containing  potassium  ferrocyanide  solution 
is  thus  obtained  attached  to  the  end  of  the  tube.  When 
it  has  become  1-2  cm.  in  diameter  it  is  detached  by 
jerking  the  tube,  and  it  then  slowly  sinks  to  the  bottom 
of  the  jar.  If  the  relative  concentrations  of  the  copper 
sulphate  and  potassium  ferrocyanide  solutions  have  been 
rightly  chosen,  the  latter  has  not  only  the  greater  density 
but  also  the  higher  osmotic  pressure.  In  virtue  of  this 
water  enters  the  bag,  dilutes  its  contents,  and  distends 
the  membrane.  The  density  of  the  contents  of  the  bag 
is  thereby  diminished,  and  as  the  water  continues  to 
enter,  it  ultimately  becomes  equal  to  and  less  than  the 
density  of  the  surrounding  copper  sulphate  solution.  That 
this  has  taken  place  is  shown  by  the  spontaneous  ascent 
of  the  bag  to  the  top  of  the  jar. 

Another  experiment  which  shows  even  more  distinctly 
the  transport  of  water  which  takes  place  across  a  semi- 
permeable  membrane  between  two  solutions  of  different 
osmotic  pressure  is  the  following.  A  small  gas  jar  is 
half  filled  with  a  copper  sulphate  solution  of  the  same 
strength  as  that  described  in  the  foregoing  experiment. 
A  narrow  straight  tube,  into  which  some  saturated  potas- 
sium ferrocyanide  solution  has  been  sucked  up,  is  closed 
at  the  top  by  a  small  piece  of  rubber  tubing  and  a 
plug  of  glass  rod.  The  tube  is  then  lowered  into  the 
copper  sulphate,  and  the  ferrocyanide  solution  is  pushed 
slightly  beyond  the  end  of  the  tube  by  compression  of 
the  rubber  tubing  with  a  screw-clip ;  a  membrane  is 
thus  obtained  hanging  from  the  end  of  the  tube  and 
separating  the  concentrated  potassium  ferrocyanide  solu- 
tion from  the  weaker  copper  sulphate  solution.  In  these 
circumstances  water  passes  from  the  copper  sulphate  to 
the  potassium  ferrocyanide.  One  result  of  this  is  that 
the  layer  of  copper  sulphate  solution  which  is  in  im- 
mediate contact  with  the  membrane  is  concentrated,  and 


56  PHYSICAL  CHEMISTRY 

becomes  denser  than  the  rest  of  the  solution;  it  there- 
fore sinks,  and,  on  account  of  the  difference  in  refractive 
power,  the  flow  or  ' trickle '  of  this  denser  solution  can 
be  readily  detected  by  the  naked  eye.  It  is  instructive 
also  to  make  a  parallel  experiment,  in  which  the  ferro- 
cyanide  solution  is  weak  and  the  copper  sulphate  solution 
is  strong.  The  ferrocyanide  solution  is  put  as  before 
into  the  tube,  which  for  the  purpose  of  this  experiment 
is  bent  so  that  the  end  immersed  in  the  copper  sulphate 
solution  points  upward.  The  water  transport  in  this 
case  is  in  the  opposite  direction,  from  the  inside  of  the 
membrane  to  the  outside.  The  copper  sulphate  solution 
in  immediate  contact  with  the  membrane  is  diluted, 
and  the  ascending  current  or  '  trickle '  of  this  lighter 
solution  is  easily  detected. 

On  these  phenomena  Tammann1  has  based  a  method 
for  finding  isotonic  solutions  of  two  membrane- forming 
salts — solutions,  that  is,  which  have  the  same  osmotic 
pressure.  With  the  help  of  an  optical  apparatus  which 
permits  the  detection  of  the  slightest  irregularity  in 
the  refractive  power  of  a  medium,  it  is  possible  to 
determine  which  one  of  a  series  of  potassium  ferrocyanide 
solutions  is  isotonic  with  a  given  solution  of  copper 
sulphate.  For  when  a  drop  of  ferrocyanide  solution 
is  introduced  into  a  copper  sulphate  solution  and  has 
surrounded  itself  with  a  membrane  there  is  a  change 
of  density,  and  therefore  of  refractive  power,  at  the  top 
or  bottom  of  the  drop,  according  as  the  copper  sulphate 
or  the  potassium  ferrocyanide  solution  has  the  greater 
osmotic  pressure.  Only  when  the  two  solutions  are 
isotonic  does  no  irregularity  occur  in  the  refractive 
index  either  at  the  top  or  the  bottom.  In  this  way 
Tammann  has  found  the  concentrations  of  the  potassium 
ferrocyanide  solutions  which  are  isotonic  with  various 

1  Ann.  Physik.,  1888,  34,  299. 


COMPAEISON  OF  OSMOTIC  PRESSURES    57 

copper  sulphate  solutions.  Some  of  his  results  are  quoted 
in  the  following  table,  the  numbers  in  which  represent 
gram-molecules  per  1000  grams  of  water.  The  two  figures 
in  the  same  horizontal  line  are  those  of  isotonic  solutions. 

CuSOi.  K4FeCy6. 

0-84  0-31 

0-68  0-24 

0-34  0-12 

0-20  0-08 

0-17  0-066 

0-094  0-036 

0-049  0-023 

The  method  may  be  extended  to  cover  other  sub- 
stances  than  these  two  salts,  so  long  as  they  do  not 
pass  through  a  copper  ferrocyanide  membrane.  Suppose, 
for  instance,  that  a  certain  solution  of  potassium  fer- 
rocyanide has  been  found  to  be  isotonic  (1)  with  a 
solution  of  copper  sulphate,  (2)  with  a  solution  of 
copper  sulphate  -f-  sucrose,  it  follows  that  the  solutions 
(1)  and  (2)  must  be  isotonic.  A  measure,  therefore,  of 
the  osmotic  pressure  of  the  sucrose  in  (2)  is  deducible 
from  the  amount  of  copper  sulphate  in  (1)  which  it 
has  replaced. 

Other  methods  which  are  available  in  comparing  the 
osmotic  effects  of  different  substances  and  in  the  dis- 
covery of  isotonic  solutions  depend  on  the  employment, 
not  of  precipitation  membranes,  but  of  certain  plant 
and  animal  membranes.  These  are  permeable  to  water 
but  impermeable  to  many  dissolved  substances,  including 
those  in  the  fluid  enclosed  by  the  membrane.  Hence, 
whenever  such  a  membrane  with  the  enclosed  fluid  is 
immersed  in  a  solution  the  osmotic  pressure  of  which 
differs  from  that  of  the  fluid,  a  passage  of  water  occurs 
in  one  direction  or  the  other  across  the  membrane. 

The   Plasmolytic   Method. — This   method   of  finding 


58  PHYSICAL   CHEMISTRY 

isotonic  solutions  of  different  substances  was  first  em- 
ployed by  the  botanist  de  Vries.1  It  depends  on  the 
contraction  exhibited  by  the  protoplasm  of  plant  cells 
when  they  are  immersed  in  a  solution  the  osmotic  pres- 
sure of  which  is  greater  than  that  of  their  own  sap. 
The  semi-permeable  extensible  membrane  or  bag  is 
the  cell  protoplasm  which  encloses  the  sap  and  clings 
closely  in  the  normal  state  to  a  surrounding  cell  wall; 
this  wall  is  relatively  rigid,  and  is  permeable  both  to 
water  and  to  dissolved  substances.  The  relation  of  the 
protoplasmic  membrane  enclosing  the  cell  sap  to  the 
surrounding  cell  wall  is  similar  to  the  relation  of  a 
football  bladder  to  the  outer  leather  covering,  with  this 
difference,  that  in  the  former  case  any  decrease  in  bulk 
of  the  bag  containing  the  cell  sap  is  followed  only  by 
a  very  slight  contraction,  and  still  slighter  change  of 
shape  of  the  cell  wall.  Hence  if  the  plant  cells  under 
observation  have  coloured  contents  any  decrease  of  pres- 
sure or  of  bulk  below  the  normal  can  readily  be  detected 
under  the  microscope,  for  the  protoplasmic  membrane 
detaches  itself  at  one  or  more  points  from  the  cell  wall — 
a  phenomenon  which,  when  brought  about  by  immersion 
in  strong  solutions,  is  known  as  '  plasmolysis.'  The 
immersion  of  turgid  cells,2  on  the  other  hand,  in  a 
solution  which  has  a  lower  osmotic  pressure  than  the 
cell  sap  produces  no  visible  result,  for  any  water 
which  enters  the  cell  merely  increases  the  pressure  in- 
side and  pushes  the  protoplasmic  membrane  if  possible 
more  closely  against  the  supporting  cell  wall. 

The  appearance  of  cells  taken  from  the  epidermis  of 
a  leaf  of  Tradescantia  discolor  when  they  are  immersed 

1  Jahrb.  wiss.   Botanik,  1884,   14,  427;   Zeit.  pTiysikal.  Chem.,  1888, 
2,415. 

2  Cells,  that  is,  which  are  in  the  natural  healthy  state, — so  full  that 
they  exert  a  stretching  force  on  the  surrounding  cell  walL 


COMPARISON   OF  OSMOTIC   PRESSURES     59 

in  solutions  of  different  strengths  is  shown  is  Fig.  6  (de 
Vries,  loc.  cit.).  The  shaded  parts  represent  the  violet 
coloured  contents  of  the  cells,  which  are  magnified  about 
300  diameters.  In  A  the  normal  condition  of  a  cell 
is  represented,  as  it  appears  when  immersed  either  in 
water  or  in  a  solution  the  osmotic  pressure  of  which  is 
lower  than  that  of  the  cell  sap — a  '  hypotonic '  solution,  as 
is  it  called.  In  B  the  condition  of  the  cell  is  represented 
as  it  appears  when  immersed  in  a  solution  containing 


FIG.  6. 

fc,  nucleus  ;  o,  plastids  ;  s,  protoplasm  stream  lines ;  j?,  protoplast ; 
h,  cell  wall.    Magnified  300  diameters. 

0*22  of  a  gram-molecule  of  sucrose  per  litre ;  plasmolysis 
has  taken  place,  the  protoplasmic  membrane  having  drawn 
away  slightly  from  the  cell  wall  at  two  points.  This 
solution  of  sucrose  must  therefore  have  an  osmotic  pres- 
sure slightly  above  that  of  the  cell  sap:  it  is  described 
as  a  'hypertonic'  solution.  In  C,  finally,  there  is  re- 
presented the  appearance  of  a  cell  when  immersed 
in  a  solution  containing  1  gram-molecule  of  potassium 
nitrate  per  litre ;  in  this  case  there  is  very  marked 
plasmolysis ;  the  salt  solution  is  strongly  hypertonic. 


60  PHYSICAL  CHEMISTEY 

A  ready  method  of  demonstrating  the  phenomenon 
of  plasmolysis  is  to  make  some  thin  shavings  of  beet- 
root, to  wash  with  water  in  order  to  remove  all  juice 
from  the  damaged  cells,  and  thereafter  to  steep  for 
some  time  in  5  per  cent,  sodium  chloride  solution.  Ex- 
amination under  the  microscope  will  then  show  that 
plasmolysis  has  taken  place.  The  occurrence  of  plasmo- 
lysis in  plant  cells  with  colourless  contents  is  rendered 
evident  by  adding  to  the  plasmolysing  salt  solution  some 
fruit  juice  or  some  vegetable  dye,  such  as  indigo  carmine 
or  aniline  blue,  which  has  no  injurious  effect  on  the 
living  substance.  The  salt  solution  if  strong  enough 
produces  plasmolysis,  the  protoplasm  retreats  from  the 
cell  wall  at  one  or  more  points,  and  is  followed  by  the 
dye,  which,  although  it  cannot  penetrate  the  protoplasm, 
can  pass  through  the  cell  wall. 

Isotonic  Coefficients. — In  order  to  get  isotonic 
solutions  of  two  salts,  it  is  necessary  to  find  that 
solution  of  the  one  salt  which  is  just  strong  enough 
to  produce  visible  plasmolysis  in  cells  of  Tradescctntia 
discolor,  Saxifraga  sarmentosa,  Begonia  manicata,  or  other 
suitable  plant.  The  corresponding  solution  of  the  second 
salt,  tested  by  means  of  cells  from  the  same  individual 
plant,  is  similarly  found,  and  the  two  solutions  are 
regarded  as  isotonic.  By  way  of  illustration  a  special 
case,  investigated  by  de  Vries,  may  be  quoted.  He 
found,  using  Tradescantia  discolor,  that  while  no  plas- 
molysis occurred  when  the  cells  were  immersed  in  a 
sucrose  solution  containing  0*20  of  a  gm.-mol.  per  litre, 
practically  all  the  cells  were  plasmolysed  when  treated 
with  a  solution  containing  0'22  gm.-mol.  per  litre.  Par- 
allel experiments  were  made  with  potassium  nitrate,  and 
it  was  found  that  the  two  corresponding  concentrations 
in  the  case  of  this  substance  were  0*12  gm.-mol.  per 


COMPARISON  OF   OSMOTIC   PRESSURES     61 

litre  and  O13  gm.-mol.  per  litre.  From  these  observa- 
tions the  conclusion  may  be  drawn  that  a  sucrose  solu- 
tion containing  O22  gm.-mol.  per  litre  is  isotonic  with 
a  potassium  nitrate  solution  containing  0*13  gm.-mol. 
per  litre.  The  ratio  of  the  isotonic  concentrations  is 
in  this  case  0'13  :  G'22^0'59,  and  it  is  clear  that  for 
equal  concentrations  potassium  nitrate  must  be  osmotic- 
ally  more  efficient  than  sucrose.  If  we  assume  with 
de  Vries  that  the  osmotic  efficiency  increases  propor- 
tionally to  the  concentration  in  each  case,  then  the 

reciprocal  of  the  foregoing  ratio,  that  is  ^=1*69,  re- 
presents the  osmotic  efficiency  of  a  potassium  nitrate 
solution  when  that  of  a  sucrose  solution  of  the  same 
molecular  concentration  is  taken  as  unity.  As  standard 
substance  de  Vries  chose  potassium  nitrate,  the  osmotic 
efficiency  of  which  he  took  as  3*0.  On  this  basis  he 
found  for  various  substances  the  following  osmotic  effi- 
ciencies, or  'isotonic  coefficients,'  as  they  were  called: 
sucrose  1-81,  glycerine  1-78,  dextrose  1*88,  tartaric  acid 
2'02,  citric  acid  2'02,  sodium  nitrate  3'0,  sodium  chloride 
3'0,  potassium  acetate  3'0,  calcium  chloride  4'33,  mag- 
nesium chloride  4*33,  potassium  citrate  5'01. 

In  finding  isotonic  solutions  of  two  substances  by  , 
the  plasrnolytic  method  the  plant  cells  play  merely  the  "" 
part  of  indicators,  and  it  is  not  necessary  to  consider 
the  osmotic  pressure  of  the  cell  contents.  It  is,  how- 
ever, pretty  evident  from  the  data  bearing  on  the  effect 
of  sucrose  solutions  on  the  cells  of  Tradescantia  discolor, 
that  the  cell  sap  in  this  case  must  have  an  osmotic 
pressure  about  equal  to  that  of  a  sucrose  solution  con- 
taining O21  gm.-mol.  sucrose  per  litre.  This  figure 
is  the  mean  of  0*20  and  0'22,  the  concentrations  of 
the  highest  hypotonic  and  the  lowest  hypertonic  solu- 
tions actually  used  in  the  observations.  It  is  not 


62  PHYSICAL  CHEMISTRY 

possible  to  fix  the  concentration  limits  more  definitely, 
for,  as  de  Vries  showed,  the  result  of  immersing  cells  of 
Tradescantia  discolor  in  a  0'21  solution  of  sucrose 
is  that  some  cells  are  plasmolysed,  others  not.  It  is 
therefore  preferable  to  take  the  mean  of  the  highest 
hypotonic  and  the  lowest  hypertonic  solution.  The 
osmotic  pressure  of  a  sucrose  solution  containing  O21 
gm.-mol.  per  litre  is,  according  to  Morse  and  Frazer's 
investigations,  about  5  atmospheres,  and  this  therefore 
must  be  approximately  the  osmotic  pressure  of  the  cell 
sap  in  the  case  of  Tradescantia  discolor  and  many  other 
plants  which  exhibit  plasmolysis  in  a  sucrose  solution 
of  about  the  same  strength. 

Applications  of  the  Plasmolytic  Method. — The  ex- 
tension of  Avogadro's  hypothesis  to  solutions  is  embodied 
in  the  statement  that  equal  volumes  of  two  solutions 
which  at  the  same  temperature  have  equal  osmotic 
pressures  contain  the  same  number  of  dissolved  mole- 
cules. Hence  if  we  are  dealing  with  two  chemically 
similar  substances  that  may  be  expected  to  have  ap- 
proximately the  same  isotonic  coefficient,  we  conclude 
that  isotonic  solutions  of  these  two  substances  will  con- 
tain per  litre  the  same  fraction  of  the  gram- 
molecular  weight.  If  the  molecular  weight  of  the 
one  substance  is  known,  that  of  the  other  may  be 
deduced  from  it.  An  interesting  application  of  this 
is  to  be  found  in  de  Vries'  original  paper.1  At  that 
time  there  was  considerable  difference  of  opinion 
as  to  the  correct  formula  for  crystallised  raffinose ;  as 
a  matter  of  fact,  three  formulae,  all  consistent  with  the 
ascertained  percentage  composition  of  the  substance, 
had  been  proposed,  viz.  C12H22On,  3H20 ;  C18H32016, 
5H20;  and  C^H^O^,  10H20.  Now  de  Vries  found 

1  Zeit.  physikal.  Chcm.,  1888,  2,  415. 


COMPARISON   OF  OSMOTIC   PRESSURES     63 

by  the  plasmolytic  method  that  a  5 '96  per  cent,  solution 
of  raffinose  was  isotonic  with  a  sucrose  solution  con- 
taining 0*1  gram-molecule  per  litre.  On  the  basis,  there- 
fore, of  Avogadro's  hypothesis  the  raffinose  solution  also 
must  contain  0*1  gram  -  molecule  per  litre ;  that  isy 
the  molecular  weight  of  raffinose  must  be  about  596. 
This  result  settles  the  question  in  favour  of  the  second 
formula,  which  requires  a  molecular  weight  of  594;. 
the  first  and  third  formulae,  on  the  other  hand,  would 
involve  molecular  weights  of  396  and  1188  respectively. 

The  plasmolytic  method  "was  originally  employed  in 
the  investigation  .of  -the  pressure  which  causes  turgidity 
(see  p.  58)  in  plant  cells,  arid  since  then  it  has  frequently 
been  applied  in  a  similar  way.  Turgidity  is  essential 
to  growth,  and  it  is  an  interesting  question  what  is  the 
pressure  prevailing  in  turgid  cells,  and  what  are  the  means 
employed  to  regulate  this  pressure  under  varying  ex- 
ternal conditions.  The  plasmolytic  method  furnishes 
the  best  means  of  arriving  at  a  solution  of  these  pro- 
blems? i/ln  order  to  apply  it  a  substance  must  first  be 
foujid  for  which  the  protoplasmic  membrane  of  the  cells 
under  .investigation  is  impermeable,  and  then  by  trial 
that  -Solution  of  the  substance  is  found  which  is  just 
able  to  produce  plasmolysis.  The  osmotic  pressure  of 
this  solution  gives  the  pressure  prevailing  in  the  cells 
and  producing  turgidity,  provided  that  the  cell  wall 
was  not  distended  in  its  normal  condition. 

How,  it  may  be  asked,  can  it  be  shown  that  the 
plasmatic  membrane  is  impermeable  or  at  least  approxi- 
mately impermeable  for  any  given  substance?  The 
guarantee  of  impermeability  in  any  particular  case  is 
found  in  the  observation  that  plasmolysis  when  once, 
produced  persists  even  when  the  cells  are  left  for  a 
considerable  time  in  the  plasmolysing  solution.  If  the 
membrane  were  slightly  permeable  to  the  substance  con- 


64  PHYSICAL  CHEMISTRY 

tained  in  the  external  hypertonic  solution,  the  plasmolysis 
would  be  only  transient ;  the  substance  would  enter  the 
cell,  and  this  would  necessarily  involve  the  passage  of  water 
in  the  same  direction,  leading  to  the  extension  of  the 
protoplasmic  membrane  and  the  disappearance  of  plas- 
molysis. If  the  membrane  were  very  highly  permeable 
to  the  substance  contained  in  the  external  solution,  it 
would  be  impossible  to  produce  plasmolysis  at  all.  These 
relationships  are  well  illustrated  by  the  behaviour  of 
certain  bacteria,1  for  example  Bacillus  cJiolcrce,  which 
are  temporarily  plasrnolysed  by  salt  and  sucrose  solutions, 
but  not  at  all  by  glycerine  solutions.  The  plasmolysis 
observed  in  the  first  case  disappears  in  the  course  of 
an  hour  or  two  as  a  rule,  showing  that  salt  and  sugar 
slowly  penetrate  the  plasmatic  membrane.  The  failure 
of  glycerine  to  produce  plasmolysis  points  to  rapid 
penetration  of  the  membrane. 

Even  when  a  substance  has  been  found  for  which  the 
membrane  is  practically  impermeable,  the  result  of  a 
plasmolytic  experiment  must  be  accepted  with  some  re- 
serve, in  so  far  as  the  osmotic  pressure  of  the  external 
plasmolysing  solution  may  not  be  equal  to  the  pressure 
prevailing  in  the  normal  cell.  For  if  the  cell  wall  in 
its  normal  state  is  stretched  or  distended,  then  as  the 
osmotic  pressure  of  the  external  solution  approaches  that 
of  the  cell  sap  the  cell  wall  must  contract ;  this  means 
that  water  is  squeezed  out  of  the  cell,  and  the  sap  be- 
comes more  concentrated.  If  we  can  imagine  the  osmotic 
pressure  of  the  external  solution  being  raised  gradually, 
this  contraction  of  the  cell  wall,  and  consequent  increase 
in  the  concentration  of  the  sap,  will  continue  until  the 
cell  wall  has  reached  its  unstretched  condition.  Any 
further  increase  in  the  external  osmotic  pressure  beyond 
this  point  will  produce  plasmolysis,  but  it  is  obvious  that 

1  See  Fischer,  Vorlesungen  tiber  Baktericn,  p.  20. 


COMPARISON  OF   OSMOTIC   PRESSURES     65 

the  cell  sap  now  in  osmotic  equilibrium  with  the  external 
solution  is,  owing  to  the  contraction  of  the  cell  wall,  more 
concentrated  than  the  sap  originally  filling  the  cell.  In 
those  cases,  therefore,  where  contraction  of  the  cell  wall 
precedes  plasmolysis,1  the  plasmolytic  values  ;are  higher 
than  those  corresponding  with  the  original  cell  sap. 

There  is  another  factor  which  must  be  taken  into 
account  in  deciding  how  far  a  plasmolytic  value  gives 
correctly  the  osmotic  pressure  of  the  cell  sap.  The  cell 
frequently  contains  substances  which  have  a  feeble  osmotic 
effect,  but  which  readily  adsorb  water.2  The  total  pres- 
sure producing  turgidity  of  the  cell,  as  given  by  the 
plasmolytic  value,  may  therefore  be  due  partly  to  the 
force  of  imbibition  and  partly  to  the  osmotic  pressure 
of  the  cell  contents.  It  is  only  when  the  first  factor 
becomes  negligible  that  the  plasmolytic  value  can  be  re- 
garded as  representing  correctly  the  osmotic  pressure  of 
the  cell  contents. 

Subject  to  these  reservations,  the  use  of  the  plas- 
molytic method  has  thrown  much  light  on  the  pressure 
which  prevails  in  plant  cells  and  on  the  extent  to  which 
this  pressure  varies  from  one  case  to  another  according 
to  the  external  conditions.  It  has  been  shown,3  for  in- 
stance, that  the  osmotic  strength  of  the  cell  sap  of 
land  plants  increases  as  the  acquisition  of  water  becomes, 
more  difficult  for  them.  For  a  bog  plant  the  isotonic 
solution  of  sodium  chloride  was  found  to  contain  0*11 
gm.-mol.  per  litre,  for  a  plant  from  sandhills  O24  gm.- 
mol.  per  litre,  for  a  plant  from  the  edge  of  a  brackish 
ditch  0'29  gm.-mol.  per  litre,  and  for  a  salt-marsh  plant 
0*51  gm.-mol.  per  litre  (  =  3  per  cent,  sodium  chloride  or 
5 '2  per  cent,  potassium  nitrate). 

1  See  Pantanelli,  Pringsheim's  Jahrb.  wiss.  Sot.,  1904,  40,  303, 
*  For  explanation  of  adsorption,  see  Chapter  XI. 
3  Drabble,  Biochem.  /.,  1907,  2,  117. 


66  PHYSICAL   CHEMISTRY 

Evidence  has,  however,  been  brought  forward  showing 
that  an  individual  plant  may  in  certain  cases  be  able 
to  vary  its  internal  osmotic  pressure  according  to  that 
of  the  surrounding  medium.  As  shown  by  Hill,1  this 
is  the  case  with  the  root  hairs  of  plants  growing  in  a 
certain  salt  marsh,  the  salinity  of  which  undergoes  marked 
variation  owing  to  periodiq  inundations  by  the  sea.  A 
sod  taken  from  this  salt  marsh  and  containing  seedlings  of 
Salicornia  Jierbacea  was  soaked  in  stream  water  for  eighteen 
hours.  Several  seedlings  taken  from  the  sod  before 
the  soaking  were  tested,  and  the  root  hairs  were  found 
to  resist  plasmolysis  in  a  5 '8  per  cent,  sodium  chloride 
solution ;  after  the  soaking,  the  root  hairs  were  plas- 
molysed  by  a  3*31  per  cent,  sodium  chloride  solution. 
Further  experiments  showed  that  the  root  hairs  of  Sali- 
cornia are  able  also  to  raise  their  internal  osmotic  strength 
in  proportion  to  the  increase  of  the  external  salinity.  The 
regulation  of  the  osmotic  pressure  may  be  effected  either 
by  chemical  changes  in  the  cell  sap  or  by  the  passage 
of  sodium  chloride  through  the  protoplasmic  membrane, 
but  it  is  uncertain  which  of  these  is  the  mechanism 
actually  employed  by  the  plant. 

Very  interesting  also  is  the  power  which  some  of  the 
lower  plants  especially  have  of  accommodating  themselves 
to  highly  concentrated  media.  This  is  notably  the  case 
with  moulds  and  bacteria ;  many  of  these  can  survive, 
and  even  grow  in,  concentrated  salt  solutions  which  would 
be  fatal  to  the  life  of  the  cell  in  the  case  of  higher 
plants.  Penicillium  and  Aspergillus  have  been  found  to 
thrive  in  solutions  the  osmotic  equivalent  of  which  is 
20  per  cent,  potassium  nitrate;  Bacillus  anthracis  flourishes 
on  agar  containing  as  much  as  8-10  per  cent,  sodium 
chloride.  Since  turgidity  is  essential  to  growth,  it  follows 
that  these  organisms  must  have  some  means  of  altering  the 
New  Phytologist,  1908,  7,  133. 


COMPARISON   OF  OSMOTIC   PRESSURES    6V 

pressure  of  their  cell  contents  according  to  the  con- 
centration of  the  surrounding  medium ;  in  this  way 
only  can  plasmolysis  be  avoided.  As  already  pointed 
out,  the  plasmatic  membrane  in  the  case  of  many  bacteria 
is  highly  permeable,  and  it  is  significant  that  the  per- 
meability is  greatest  in  the  case  of  those  bacteria  which 
are  best  able  to  thrive  in  concentrated  media.  Per- 
meability of  the  membrane  does  not  however  appear  to  be 
responsible  for  the  power  of  accommodation  exhibited  by 
moulds;  in  this  case  increase  in  the  concentration  of 
the  external  medium  is  balanced  by  the  production  of 
osmotically  active  substances  in  the  cell  itself  through 
the  agency  of  metabolic  change.1 

Although  some  of  these  lower  organisms  have  such 
a  marked  power  of  accommodating  themselves  to  ex- 
ceptional osmotic  conditions,  sudden  transference  from 
a  very  dilute  to  a  very  concentrated  solution  or  vice  versa 
may  have  serious  consequences  for  the  cell.  This  is 
specially  obvious  in  cases  where'  the  cell  has  accom- 
modated itself  to  a  highly  concentrated  solution  of  a 
substance  capable  of  passing  only  slowly  through  the 
membrane;  the  result  of  immersing  such  a  cell  all  at 
once  in  pure  water  is  to  burst  it.  If  algae,  for  instance, 
are  immersed  in  an  isotonic  solution  of  glycerine,  and 
the  latter  is  allowed  to  evaporate  until  its  concentration 
rises  to  about  50  per  cent.,  no  plasmolysis  will  be  observed 
at  any  time ;  the  glycerine  penetrates  rapidly  enough 
to  prevent  this,  and  the  rise  of  osmotic  pressure  in  the 
cell  keeps  pace  with  the  increase  of  the  external  con- 
centration. On  immersion  in  water  the  glycerine  begins 
to  pass  out,  but  its  escape  is  far  too  slow  to  neutralise 
the  enormous  pressure  difference  between  the  two  sides 
of  the  membrane,  and  the  cell  therefore  bursts.  The 

1  Von  Mayenburg,  Pringsheim's  Jahr.  wiss.  Bot.,  1901,  36,  381. 


68  PHYSICAL  CHEMISTRY 

frequent  disruption  of  pollen  grains  which  fall  into 
water  is  similarly  due  to  osmotic  causes. 

The  value  of  the  plasmolytic  method  has  lately  been 
questioned  by  Osterhout.1  In  experiments  with  Vaucheria 
he  found  that  plasmolysis  occurred  with  a  sodium  chloride 
solution  as  dilute  as  O0001N;  the  addition  of  calcium 
chloride  however  to  the  sodium  chloride  solution, 
although  it  raises  the  osmotic  pressure,  prevents  the 
contraction  of  the  protoplasm  from  the  cell  walls.  If 
1  molecule  of  calcium  chloride  is  present  for  every 
100  molecules  of  sodium  chloride,  the  cells  may  be 
immersed  in  0*1N  sodium  chloride  solutions  without 
suffering  plasmolysis.  It  looks  therefore  as  if  in  some 
cases  at  least  sodium  chloride  exerts  a  specific  effect 
on  the  protoplasm,  bringing  about  a  contraction  which 
is  indistinguishable  from  plasmolysis  caused  by  purely 
osmotic  action. 

Blood  Corpuscles  and  Isotonic  Solutions. — The  red 

blood  corpuscle  is  a  cell,  the  contents  of  which  are 
enclosed  in  a  delicate  extensible  membrane,  permeable 
to  water  but  impermeable  to  many  dissolved  substances. 
There  is,  however,  no  cell  wall  to  give  support  to  the 
membrane,  so  that  when  red  blood  corpuscles  are  im- 
mersed in  water,  they  first  swell  up  in  consequence  of 
the  osmotic  pressure  and  then  burst.  This  disruption 
of  the  membrane  allows  the  colouring  matter,  the 
haemoglobin,  to  escape,  and  the  water  assumes  a  deep 
red  colour:  the  corpuscles  are  said  to  be  'laked.'  If 
now  a  few  drops  of  defibrinated  blood  are  added  to 
each  of  a  series  of  solutions  of  sodium  chloride  of 
gradually  increasing  strength,  contained  in  test-tubes, 
the  result  obtained  for  all  the  solutions  up  to  a  certain 
limiting  concentration  is  similar  to  that  observed  in 

1  Bot.  Gazette,  1908,  46,  53. 


COMPARISON  OF  OSMOTIC   PRESSURES    69 

the  case  of  water ;  after  sufficient  time  has  been  allowed 
for  sedimentation,  it  is  seen  that  while  the  bottom  of 
the  tube  may  have  a  deposit  of  corpuscles  or  their 
transparent  envelopes,  the  supernatant  liquid  is  red. 
In  all  the  solutions,  on  the  other  hand,  which  are  above 
the  limiting  concentration,  the  corpuscles  have  settled 
to  the  bottom,  and  the  supernatant  liquid  is  colourless. 
Similarly,  a  limiting  concentration  may  be  discovered  for 
another  salt,  that  solution  being  found  by  trial  which 
is  just  dilute  enough  to  lake  the  corpuscles.  The  solu- 
tions then  of  the  two  salts  which  are  equivalent  in  osmotic 
effect,  as  indicated  by  the  incipient  laking  of  the  cor- 
puscles, are  to  be  regarded  as  isotonic  solutions. 

Hamburger,  who  is  responsible  for  this  method  of 
determining  isotonic  concentrations,  records  the  following 
figures,1  which  show  how  far  it  is  possible  in  ordinary 
work  to  draw  a  definite  line  between  solutions  which 
lake  the  corpuscles  and  those  which  do  not.  The  figures 
in  Column  I.  represent  the  lowest  percentage  concen- 
tration at  which  the  corpuscles  sink  to  the  bottom  and 
leave  the  supernatant  liquid  absolutely  colourless ;  the 
figures  in  Column  II.  are  the  highest  percentage  con- 
centrations at  which  the  corpuscles  when  they  settle 
leave  the  supernatant  liquid  red.  Bullock's  blood  was 
used  in  these  experiments. 

Substance.  I.  II. 

KNO3 1-04  0-96 

NaCl 0-60  0-56 

K2S04 M6  1-06 

C12H22°11 6'29  6'63 

CH3.COOK      ....     1'07  1-00 

MgSO4.7H2O  ....     3-52  3-26 

CaCl2 0-85  0-79 

By  careful  work  it  is  possible  to  bring  the  limits  even 
1  Zeit.  physikal.  Chem.,  1890,  6,  319. 


70  PHYSICAL   CHEMISTKY 

closer  than  is  shown  in  the  table,  but  for  ordinary  pur- 
poses it  is  sufficient  to  take  as  the  critical  concentration 
for  each  substance  the  mean  of  the  two  figures  quoted 
above. 

It  is  perhaps  necessary  to  point  out  that  a  1  per  cent, 
solution  of  potassium  nitrate,  which  is  a  critical  con- 
centration so  far  as  the  corpuscles  of  bullock's  blood 
are  concerned  (see  above  table),  is  not  isotonic  with  the 
contents  of  these  corpuscles  in  their  normal  condition. 
If  the  corpuscles  are  immersed  in  a  salt  solution  which 
is  isotonic  with  their  contents,  and  if  the  salt  solution 
is  then  gradually  diluted,  the  corpuscles  undergo  a 
corresponding,  increase  in  bulk,  until  at  last  the  limit 
of  resistance  of  the  membrane  is  reached ;  the  bursting 
is  the  final  stage  in  the  progressive  distension  of  the 
corpuscle  membrane,  and  occurs  at  a  concentration  con- 
siderably below  that  which  is  isotonic  with  the  corpuscle 
contents  in  their  normal  condition. 

Light  is  thrown  on  this  question  by  determining  the 
concentration  of  the  potassium  nitrate  solution  that 
is  isotonic  with  blood  serum.  Hamburger  showed  that 
a  mixture  of  10  cub.  cm.  horse  blood  serum  with  7 
cub.  cm.  of  water  was  unable  to  lake  certain  blood 
corpuscles,  although  laking  took  place  when  7*5  cub.  cm. 
of  Water  was  mixed  with  10  cub.  cm.  of  the  serum- 
Corpuscles  from  the  same  source  were  laked  by  0*96 
per  cent,  potassium  nitrate  solution,  but  not  by  0'97 
per  cent,  solution.  Hence  a  mixture  of  10  cub.  cm. 
serum  •-}-.  7*25  cub.  cm.  of  water  is  isotonic  with  a  0'965 
per  cent,  solution  of  potassium  nitrate,  and  we  may 
conclude  that  the  potassium  nitrate  solution  which  would 
be  isotonic  with  the  undiluted  serum  would  contain 

0-965^5  =  1-66  per  cent,  of  the  salt.  The  corpuscles 
of  horse  blood  are  in  osmotic  equilibrium  with  the  serum. 


COMPARISON  OF  OSMOTIC  PRESSURES    71 

so  that  no  great  error  can  be  made  in  regarding  the 
contents  of  these  corpuscles  as  isotonic  with  a  1*66 
per  cent,  solution  of  potassium  nitrate.  This  is  quite 
different  from  the  most  concentrated  solution  of  potassium 
nitrate  that  is  able  to  lake  horse  blood  corpuscles;  that 
solution  contains  about  1/17  per  cent,  of  the  salt. 

It  is  noteworthy  that  the  limiting  concentrations  of 
a  salt  which  produce  laking  of  blood  corpuscles  are 
different  for  different  kinds  of  blood.  Thus,  for  example, 
the  highest  concentration  of  sodium  chloride  which  causes 
laking  is  O21  per  cent,  for  frog's  blood,  0'47  per  cent, 
for  human  blood,  and  0*68  per  cent,  for  horse  blood. 
It  is  probable  that  these  differences  are  connected  not 
so  much  with  the  varying  osmotic  strength  of  the 
corpuscle  contents,  as  with  the  different  resisting  power 
of  the  membrane./ 

Isotonic  Solutions  found  by  the  Hsematocrit. — Blood 
corpuscles  may  be  used  in  another  way  for  the  purpose 
of  finding  isotonic  solutions.  It  has  already  been  pointed 
out  that  corpuscles  immersed  in  solutions  of  gradually 
diminishing  concentration  increase  in  bulk,  until  ulti- 
mately the  membrane  gives  way.  If,  on  the  other  hand, 
they  are  immersed  successively  in  solutions  of  higher 
and  higher  concentration,  more  and  more  water  passes 
out  through  the  membrane,  and  the  volume  of  the  cor- 
puscles diminishes.  It  is  evident  that  there  must  be 
for  each  salt  which  cannot  penetrate  the  membrane  some 
concentration  such  that  corpuscles  immersed  in  the  solu- 
tion undergo  no  change  of  volume.  This  solution  is 
discovered  with  the  aid  of  the  haematocrit,1  a  graduated 
thermometer  tube  which  can  be  fitted  to  a  centrifuge, 
and  in  which  the  corpuscles  collect  when  blood,  either 
alone  or  mixed  with  salt  solution,  is  centrifuged.  A 

1  See  Hedin,  Zeit.  physikal.  Chem.,  1895,  17,  164. 


72  PHYSICAL   CHEMISTRY 

definite  quantity  of  blood,  say  10  cub.  cm.,  is  treated  in 
this  way,  and  the  operation  is  continued  until  no  further 
diminution  in  the  volume  of  the  corpuscles  in  the  hEemato- 
crit  can  be  detected.  The  same  quantity  of  blood  is 
then  mixed  with  each  of  a  series  of  salt  solutions  of 
graded  strength,  and  the  volume  of  the  corpuscles  in 
each  mixture  is  determined  as  before.  That  solution  in 
which  the  volume  of  the  corpuscles  is  the  same  as  in 
the  blood  itself  is  thus  discovered;  let  it  be  designated 
as  A.  Similarly,  out  of  a  series  of  solutions  of  another 
salt  one  B  is  found,  in  which  also  the  volume  of  the 
corpuscles  is  unaltered.  This  being  so,  A  and  B  are 
isotonic  solutions,  and  from  the  isotonic  concentrations 
the  isotonic  coefficients  may  be  calculated  as  already 
shown. 

It  is  interesting  to  compare  the  values  of  the  isotonic 
coefficients  obtained  by  different  methods  for  various 
substances.  This  is  done  in  the  following  table,  where 
the  isotonic  coefficients  are  referred  to  that  of  sucrose 
taken  as  unity  :  — 


Plasmolytic  e          Hfcm*tocrit 

Method.  Oscle  Method> 


Cr,H,oOn   ...  I'OO  TOO  I'OO 

MgSO4.    ...  1-09  1-27  1-10 

KNO3  ....  1-67  1-74  1-84 

NaCl     ....  1-69  1-75  1-74 

CH3.COOK     .     .  1-67  1-66  1-67 

CaCl2     ....  2-40  2-36  2'33 

The  concentration  of  the  sodium  chloride  solution  in 
which  the  volume  of  the  corpuscles  is  unaltered  is  ap- 
proximately the  same  for  all  mammalian  blood,  namely, 
O9  per  cent.  To  this  solution  the  term  'physiological 
salt  solution  '  may  properly  be  applied,  for  it  is  the  solu- 
tion in  which  the  corpuscles  of  mammalian  blood  remain 
unaltered  as  to  volume,  and  in  which,  therefore,  they 


COMPARISON   OF  OSMOTIC   PRESSURES    73 

may  be  preserved.  The  term  '  physiological  salt  solution ' 
is  sometimes  understood  to  mean  a  0'6-0'T  per  cent, 
sodium  chloride  solution,  but  this  is  a  solution  in  which 
mammalian  blood  corpuscles  certainly  undergo  alteration. 
The  lower  figure  has  its  origin  in  the  fact  that  experi- 
ments of  this  kind  were  first  made  with  frog's  blood, 
the  osmotic  pressure  of  which  is  equal  to  that  of  a  0*6  or 
0*65  per  cent,  solution  of  sodium  chloride. 

Some  Effects  produced  by  HyjJertonic  Solutions.— 

The  facts  discussed  in  the  earlier  part  of  this  chapter 
show  that  when  a  plant  or  animal  cell  is  immersed  in  a 
hypertonic  solution  of  a  substance  which  cannot  enter 
the  cell,  water  passes  outwards,  and  the  contents  of  the 
cell  become  more  concentrated.  Such  a  change  of  con- 
centration may  markedly  affect  the  activity  of  the  cell, 
as  instanced  by  the  following  case.  The  formation  of 
starch  from  sugar  that  occurs  in  many  plant  cells,  takes 
place  only  when  the  concentration  of  the  sugar  has 
reached  a  certain  limit.  It  is  found,  however,  that  even 
in  cells  in  which  the  sugar  concentration  is  just  short 
of  that  limit,  starch  formation  can  be  induced  by  plas- 
molysing  with  potassium  nitrate.  The  effect  of  the 
hypertonic  potassium  nitrate  solution  is  to  raise  the  con- 
centration of  the  cell  contents  beyond  the  minimum 
necessary  for  the  production  of  starch. 

Another  interesting  example  of  an  osmotic  stimulus  is 
found  in  the  part  which  hypertonic  solutions  play  in 
artificial  parthenogenesis.1  Loeb  has  shown  that  when 
unfertilised  eggs  of  the  sea-urchin  Strongylocentrotus 
purpuratus  are  placed  for  1J-2  minutes  in  a  mixture  of 
50  cub.  cm.  sea-water  +  3  cub.  cm.  0*1N  butyric  acid 
(or  other  monobasic  fatty  acid),  and  are  then  put  back 

1  See  Loeb,  Die  chcmische  EntwicTdungserregung  des  tierischen  L'ies, 
1909;  also  Zeit.  physikal.  Chem.,  1910,  70,  220. 


f 

74  PHYSICAL  CHEMISTRY 

f 
in  ordinary  sea-water,  a  fertilisation  membrane  is  fui^ 

in  all  cases,  the  appearance  of  which  marks  the  firut  stage 
of  development  of  the  eggs.  One  method  of  continuing 
this  artificial  development  is  to  place  the  eggs,  after 
the  formation  of  the  membrane,  in  hypertonic  sea-water 
(e.g.  50  cub.  cm.  sea-water  +  8  cub.  cm.  2'5N  NaCl). 
When  they  have  been  allowed  to  remain  20-50  minutes 
in  this  hypertonic  sea-water  the  eggs  are  placed  in  normal 
sea-water,  and  there  develop  into  larvas.  It  is  a  very 
interesting  fact  that  a  hypertonic  sucrose  solution  may  be 
employed  instead  of  hypertonic  sea- water;  the  result  is 
the  same  so  far  as  the  development  of  the  eggs  is  con- 
cerned. It  is  not  quite  certain  how  the  hypertonic 
solution  exerts  its  influence  in  this  case,  but  probably  it 
facilitates  the  oxidation  of  certain  substances  which,  if 
not  removed,  would  lead  to  cytolysis. 


CHAPTER   V 

PERMEABILITY    AND    IMPERMEABILITY    OF 
MEMBRANES 

How    does    a    Semi-permeable    Membrane     Act?— 

The  consideration  of  osmotic  phenomena  leads  very 
obviously  to  the  questions:  Wherein  lies  the  efficiency 
of  a  semi- permeable  membrane?  Why  is  a  membrane 
permeable  to  one  substance,  impermeable  to  another? 
The  answers  to  these  questions  have  a  direct  bearing 
not  only  on  the  purely  physical  side  of  osmotic  pres- 
sure, but  also  on  the  osmosis  which,  'as  indicated  in 
the  previous  chapter,  plays  such  an  important  part  in 
the  equilibrium  between  plant  and  animal  cells  and 
their  surroundings.  The  best  method,  perhaps,  of  deal- 
ing with  this  problem  is  first  to  consider  it  in  its 
physical  aspect  alone,  and  then  see  how  far  the  infor- 
mation so  obtained  can  help  in  the  interpretation  of 
the  biological  phenomena  of  osmosis. 

According  to  Jraube,1  who  discovered  and  studied 
various  precipitation  ^membranes,  such  as  copper  fer- 
rocyanide  and  gelatin-tannin,  the  feature  of  a  semi- 
permeable  membrane  which  enables  it  to  differentiate 
between  one  substance  and  another  is  the  size  of  its 
molecular  interstices.  Acting  like  a  sieve,  the  mem- 
brane prevents  the  passage  of  particles  which  have  a 
relatively  large  volume.  Traube  indeed  maintained  that 
with  the  help  of  these  precipitation  membranes  it  would 

1  Archiv.  Anat.  PhysioL,  1867,  87. 
76 


76  PHYSICAL  CHEMISTRY 

be  possible  to  estimate  the  relative  size  of  the  particles 
of  dissolved  substances. 

It  is  certainly  the  case  that  the  substances  which  are 
suited  for  quantitative  experiments  on  osmotic  pressure, 
substances  therefore  which  must  be  practically  incapable 
of  penetrating  the  membrane  employed,  are  all  charac- 
terised by  a  high  molecular  weight.  The  compounds 
which  have  figured  in  direct  determinations  are  mainly 
carbohydrates  or  ferrocyanides,  and  this  fact,  if  one 
assumes  with  Traube  that  the  volume  of  a  molecule 
depends  on  its  weight  and  its  complexity,  seems  to 
support  his  conception  of  the  action  of  the  membrane. 

There  are  however  many  other  facts  which  are  opposed 
to  this  "sieve  theory  of  the  membrane*!  In  an  investi- 
gation of  the  permeability  of  gelatin-tannin,  zinc  ferro- 
cyanide,  and  copper  ferrocyanide,  Tammann  found  l  that 
of  17  dyes  tested  11  penetrated  the  first  membrane, 
7  the  second,  and  5  the  third.  On  the  basis  of  the 
sieve  theory  this  would  mean  that  the  interstices  or 
pores  were  widest  in  the  gelatin-tannin  membrane  and 
narrowest  in  the  copper  ferrocyanide  membrane.  But 
with  individual  dyes  it  was  found  that  in  some  cases 
the  copper  ferrocyanide  membrane  was  more  permeable 
than  the  zinc  ferrocyanide,  in  other  cases  the  latter  was 
more  permeable  than  the  gelatin- tannin  membrane,  a 
result  quite  inconsistent  with  the  sieve^theory.2 

Again,  Raoult3  found  that  when  methyl  alcohol  and 
ether  are  separated  by  a  membrane  consisting  of  pig's 
bladder,  there  is  an  osmotic  flow  from  the  alcohol  to 
the  ether.  If,  however,  the  two, liquids  are  separated 
by  a  membrane  of  vulcanised  c^ufenouc,  osmosis  takes 
place  in  the  opposite  direction,  that  is,  from  the  ether 
to  the  alcohol.  There  must,  therefore,  be  some  other 

1  Zeit.  physikal.  Ckeni.,  1892,  10,  255.       *  §ee,  however,  pp.  199,  200. 
3  Zeit.  physikal.  Chem.,  1895,  17,  737. 


PERMEABILITY  AND   IMPERMEABILITY    77 

factor    involved   besides   the   size   of  the  pores   in   the 
membrane. 

The  nature  of  this  factor  is  clearly  indicated  by  Tam- 
mann's  experiments,1  which  showed  that  pig's  bladder 
absorbs  ten  times  as  much  methyl  alcohol  as  ether, 
and  that  dk&tftcKpii^  absorbs  about  one  hundred  times 
as  much  ether  as  methyl  alcohol.  The  direction  of  the 
osmQtic_flow-4s-therefore  determined  byjthe  preferential 
absorption_o£-^Be-o£  -the^  twa  liquids  by  the  membrane. 
This  result  was  established  more  definitely  by  Flusin,2 
who  measured  the  velocity  with  which  water,  methyl 
alcohol,  and  amyl  alcohol  pass  through  pig's  bladder,  when 
the  other  side  is  bathed  by  ethyl  alcohol,  and  when  the 
pressure  remains  equal  on  the  two  sides  of  the  membrane. 
Ethyl  alcohol  was  taken  as  the  second  liquid  in  all  cases, 
because  the  bladder  is  practically  impermeable  to  this 
liquid.  Some  of  Flusin's  results  are  given  in  the  follow- 
ing table ;  the  figures  under  '  velocity '  represent  the 
volume  of  the  liquid  in  cub.  mm.  which  passed  per 
hour  across  1  sq.  dcm.  of  surface,  and  the  figures  under 
*  absorption '  are  the  volumes  of  each  liquid  absorbed 
by  100  grams  of  bladder  in  five  minutes. 

Liquid.                                  Velocity.  Absorption. 

Water 4674  121 '9 

Methyl  alcohol    ....     1748  287 

Amyl  alcohol 646  7*2 

The  view  that  ±he  comp§rative__permeability  or  im- 
permeability of  a_membrane  to__  different  substances 
depends  ^on  its  power  to  dissolve  or ...  absorb-them  to  a 
greatex_Qr_Jess  extjent_  finds  support  in  the  fact  that 
it  is  possible  to  construct  osmotic  cells  in  which  absorp- 
tion by  the  membrane  is  undoubtedly  the  ruling  factor. 
Reference  may  be  made  in  this  connection  to  the  experi- 

1  Zeit.  physikal.  Chem.,  1897,  22,  490. 

2  C&mpt  rend.,  1898,  126,  1497;  1900,  181,  1308. 


78  PHYSICAL  CHEMISTRY 

ment  described  on  p.  24.  This  experiment,  which  fur- 
nishes an  example  of  gaseous  osmosis,  showed  that  in 
a  cell  containing  air  and  closed  by  a  membrane  im- 
pregnated with  water,  extra  pressure  is  developed  when 
the  outside  of  the  membrane  is  bathed  by  a  gas  soluble 
in  water.  More  definite  shape  is  given  to  this  argu- 
ment from  gaseous  osmosis  by  Sir  William  Kamsay's 
work  on  the  pressure  produced  by  the  passage  of 
hydrogen  through  a  palladium  septum.1  In  these  ex- 
periments the  outside  of  a  small  palladium  cell  con- 
taining nitrogen  was  bathed  by  a  current  of  hydrogen. 
The  apparatus  was  kept  at  280°  by  means  of  a  vapour 
jacket,  and  the  inside  of  the  palladium  tube  was 
connected  with  a  manometer  to  register  the  pressure. 
When  the  initial  pressure  in  the  cell  was  1  atmosphere, 
and  a  current  of  hydrogen  (at  atmospheric  pressure) 
had  been  passed  for  some  time,  the  internal  pressure 
rose  to  about  1*9  atmosphere.  This  increment  of  pres- 
sure in  the  cell,  although  just  nine-tenths  of  what  might 
be  expected,  is  plainly  connected  with  the  well-known 
power  of  palladium  to  absorb  hydrogen,  as  distinct 
from  other  gases ;  the  palladium  septum  by  its  absorp- 
tive power  differentiates  between  hydrogen  arid  other 
gases,  and  so  gives  rise  to  osmotic  phenomena.  /  ^  \j 

Another  osmotic  cell,  the  efficiency  of  which  clearly 
depends  on  selective  absorption  or  pnlnt.i'nn-Jay-JJw-^ftm- 
brane,  is  one  described  by  Crum  Brown.2  Phenol  and 
water  are  shaken  up  together  until  two  mutually  satu- 
rated layers  are  obtained,  namely,  (1)  a  lighter  layer 
containing  excess  of  water,  (2)  a  layer  containing  excess 
of  phenol.  In  a  portion  of  the  liquid  from  layer  (1) 
a  quantity  of  nitrate  of  lime  is  dissolved  sufficient  to 
make  the  solution  heavier  than  layer  (2).  This  solution 

1  Phil.  Mag.,  1894,  38,  206. 

2  Proc.  Roy.  Soc.  Edin.,  1899,  22,  439. 


PERMEABILITY  AND   IMPERMEABILITY    79 

is  then  put  at  the  bottom  of  a  narrow  cylindrical  jar, 
and  above  it  there  is  carefully  poured  a  small  quantity 
of  layer  (2),  say  about  6-8  mm.  in  thickness.  Above 
this  again  is  put  a  considerable  quantity  of  layer  (1). 
The  bottom  layer  in  the  cylinder  is  to  be  regarded  as 
the  top  layer  +  calcium  nitrate,  and  the  two  are  separated 
by  a  liquid  septum  in  which  phenol  predominates,  and 
in  which  calcium  nitrate  is  very  sparingly  soluble.  The 
medium,  however,  in  which  the  calcium  nitrate  is  dis- 
solved is  readily  soluble  in  the  liquid  septum,  as  appears 
from  the  fact  that  phenol  and  water  are  appreciably 
miscible.  Hence  in  the  cylinder  there  is  a  solution 
separated  from  its  solvent  by  a  septum  which  is  per- 
meable to  the  solvent,  but  nearly  impermeable  to  the 
dissolved  substance.  The  natural  result  is  that  the 
bulk  of  the  solution  gradually  increases  at  the  expense 
t)f  the  solvent,  and  the  intervening  liquid  septum  slowly 
moves  up  the  cylinder.  Here  again  we  have  a  case 
in  which  osmosis  undoubtedly  depends  on  selective 
absorption  by  the  membrane. 

The  physical  evidence  which  has  just  been  quoted 
gives  strong  support  to_jthe  jvjew^bhat  the  efficiency  of 
a  ^e^mi-penneable^  mejnbrane^-  depends  on  its  ability  to 
differentiate,  by^-solvent  or  absorptive  power,  between 
the___sjibstances  which  seek  to  penetrate  it.  We  may 
next  inquire  how  far  this  view  can  interpret  the  infinitely 
more  complex  phenomena  connected  with  the  permea- 
bility and  impermeability  of  living  membranes.  The 
attempt,  however,  to  give  any  such  interpretation  de- 
mands first  a  more  detailed  discussion  of  the  experimental 
evidence  bearing  on  the  problem,  evidence  supplied 
mainly  by  Overton's  work.1 

1  Vierteljahrschrift  Zurich,  1895,40,  199  ;  1899,  44,  88;  Zeit.  physical 
Chem.,  1897,  21,  189 ;  Jahrb.  wiss.  Botanik,  1899,  34,  669. 


80  PHYSICAL   CHEMISTEY 

Permeability  of  Living  Membranes. — Overtoil's  ex- 
periments on  the  permeability-of  living  membranes  were 
made  chiefly  with  plant  cells,  but  there  is  remarkable 
agreement  between  the  behaviour  of  plant  and  animal 
membranes  in  this  respect,  and  it  is  true  generally  that 
a  chemical  compound  which  can  penetrate  the  protoplasm 
of  a  plant  cell  is  capable  of  doing  so  in  the  case  also 
of  an  animal  cell.  The  first  method  employed  by  Overton 
in  the  systematic  study  of  permeability  was  the  plas-. 
molytic  one  discussed  in  the  previous  chapter,  but  it  is 
necessary  to  describe  rather  more  in  detail  the  procedure 
actually  adopted ;  this  is  best  done  by  reference  to  a 
particular  case. 

When  rgpt  hairs  of  H/ydrodiaris  are  immersed  in  a 
7l5_per_cent._sucrose  solution  distinct  plasmolysis  occurs, 
although  none  is  observed  in  a  7  per  cent,  solution. 
Further,  if  the  7'5  per  cent,  solution  in  which  the  hairs  are 
immersed  is  prevented  from  becoming  more  concentrated  by 
evaporation,  the  extent  of  plasmolysis  remains  unchanged 
over  a  period  of  twenty-four  hours.  The  plasmolysis 
vanishes  instantaneously  when  the  hairs  are  dipped  in 
pure  water,  and  reappears  with  equal  readiness  when 
they  are  replaced  in  the  7 '5  per  cent,  sucrose  solution. 
The  fact  that  the  protoplasmic  streaming  continues  un- 
abated while  the  hairs  are  in  this  solution  shows  that 
sucrose  exerts  no  injurious  effect  on  the  vitality  of  the 
cells.  Similar  results  are  obtained  with  solutions  of  other 
substances  as  well  as  sucrose,  and  the  conclusion  is  that 
the  protoplasmic  membrane  is  strictly  semi-permeable  in 
these  cases.  There  are  however  many  compounds  which, 
although  without  deleterious  influence  on  tEe  plant,  are 
unable_jbojproduce  jplasmolysis,  or,  at  the  most,  produce 
a  temporary  plasmolysis.  Ethy l_alcohol  is  an  example 
of  a  chemical  compound  for^which  the  protoplasmic 
membrane  is  highly  permeable,  an3~wEich  therefore  is 


PERMEABILITY   AND   IMPERMEABILITY     81 

unable  to  produce  plasmolysis.  If  a  Hydrocharis  root 
is  placedTTrfa^solution  containing  7  per  cent,  of  sucrose 
+  3  per  cent,  of  ethyl  alcohol,  no  plasmolysis  occurs, 
although  this  solution  is  isotonic  with  a  28  per  cent, 
sucrose  solution.  The  failure  of  the  cells  to  make  any 
plasmolytic  response  cannot  be  due  to  any  injurious 
influence  of  the  alcohol,  for  this  compound  in  3  per 
cent,  solution  leaves  the  majority  of  plant  cells  un- 
harmed, except  after  prolonged  contact. 

Similar  to  alcohol  in  the  power  of  rapid  penetration 
are  all  monohydric  alcohols,  aldehydes,  ketones,  and  esters. 
The  dihydric  alcohols  and  the  amides  of^monobasic  acids 
penetrate  the  cell  membrane  more  slowly,  and  the  per- 
meability is  still  less  for  glycerine  and  urea.  In  the 
case  of  the  hexahydric  alcohols,  the  hexoses,  the  amino- 
acids,  and  neutral  salts  of  the  organic  acids,  the  permea- 
bility is  inappreciable. 

In  some  cases  another  method  of  studying  the  permea- 
bility of  the  cell  membrane  was  employed  by  Overton. 
The  sap  of  many  plant  cells  contains  tannin,  a  substance 
which  forms  sparingly  soluble  precipitates  with  numerous 
chemical  compounds ;  hence  when  cells  containing  tannin 
are  dipped  in  an  aqueous  solution  of  one  of  these  com- 
pounds, the  greater  or  smaller  permeability  of  the  proto- 
plasmic membrane  betrays  itself  by  the  more  or  less 
rapid  formation  of  a  precipitate  in  the  cell.  In  his  ex- 
periments with  caffeine  Overton  found  that  the  quantity 
of  precipitate  formed  inside  SyzLrogyra  cells  increased 
with  the  concentration  of  the  external  solution,  while 
if  cells  containing  precipitate  were  placed  successively  in 
caffeine  solutions  of  gradually  decreasing  concentration, 
the  precipitate  grew  less  and  less.  The  caffeine,  in  fact, 
penetrates  the  protoplasm  with  ease,  and  this  is  the  case 
also  with  ammonia,  aliphatic  amines,  and  free  alkaloids ; 
for  the  salts  of  the  alkaloids,  however,  the  membrane 


82  PHYSICAL  CHEMISTRY 

is  less  permeable,  and  to  this  fact  is  probably  due  the 
weaker  toxic  action  of  these  salts  compared  with  that  of 
the  free  alkaloids. 

Another  large  class  of  substances,  the  behaviour  of 
which  in  relation  to  the  living  membrane  is  interesting, 
is  that  of  the  organic  dye-stuifs.  Emphasis  was  laid  by 
4  Overton  on  the  fact  that  the  salts  of  the  basic  aniline 
dyes,  e.g.  methylene  blue,  are  as  a  rule  very_jeadily_  taken 
up  by  the  plant  or  animal  cell,  whereas  those  which 
are  sulphonic  acid  salts,  e.g.  indigo  carmine,  either  cannot 
penetrate  the  cell  membrane  at  all,  or  do  so  with  great 
difficulty. 

Consideration  of  all  these  facts  led  Overton  to  the  view 
that,  so  far  as  the  living  membrane  can  be  regarded 
'  from  the  purely  physical  standpoint,  it  is  selective 
absorption_onthe  j>art_of  the  membrane  which  deter- 
mines^ the  ability  or  inability  of  any  substance  to  enter 
thB=cell.  The  compounds  to  which  the  cell  membrane 
is  permeable  are  generally  soluble  in  fatty  oils,  and  it 
probably  consists  of  a  substance  which  resembles  these 
in  solvent  power.  Overton  maintains  that  the  surface 
layer  of  the  protoplast  is  impregnated  with  cholesterol 
or  a  mixture  of  cholesterol  with  other  compounds,  such  as 
\  lecithin,  and  that  the  ability  of  a  substance  to  make  its 
way  into  the  cell  depends  on  its  solubility  in  cholesterol. 
In  support  of  this  contention  it  has  been  found  that 
there  is  a  distinct  parallelism  between  the  rapidity  with 
which  various  substances  penetrate  the  cell  and  the  extent 
of  their  solubility  in  cholesterol  and  lecithin  solutions. 
Overton  finds,  for  instance,  that  the  basic  aniline  dyes  are 
readily  dissolved  by  solutions  of  cholesterol  and  lecithin, 
but  that  the  sulphonic  acid  dyes,  to  which  the  cell  mem- 
brane is  generally  impermeable,  are  very  sparingly  soluble 
in  these  media. 

This   theory   of   the(lipoid    nature   of    the    plasmatic 


PERMEABILITY   AND   IMPERMEABILITY     83 

membraye  has  been  very  widely  accepted,  but  it  is  not 
in  all  respects  satisfactory;  it  fails,  for  instance,  to 
give  a  reasonable  interpretation  of  the  fundamental  fact 
that  the  membrane  of  plant  and  animal  cells  is  so  readily 
permeable  to  water.  If,  in  reply  to  this  objection,  it 
is  maintained  that  some  of  these  lipoids  are  able  to 
take  up  appreciable  quantities  of  water,1  one  may  ask : 
How  is  it,  then,  that  simple  inorganic  salts  are  unable 
to  penetrate  the  membrane,  or  that  part  of  it  which 
is  so  impregnated  with  water?  In  this  connection  it  is 
noteworthy  that  Czapek's  work  on  the  surface  tension  of 
the  plant  cell  (see  p.  85#)  is  opposed  to  the  view  that  the 
\  plasmatic  membrane  is  a  continuous  Irppid  film,\and  rather 
lavours  the  conception  oflt  as  a  verylme  fat  emulsion, 
permeable  for  water  and  substances  soluble  in  water. 

The  theory  has  been  criticised  adversely  by  Ruhland,2 
who  contends  that  the  (parallelism  between  power  to 
penetrate  the  protoplasmic  membrane  and  solubility  in 
cholesjigrol  solutions  is  not  so  complete  as  Overton  be- 
lieves. There  ""are  dyes  which  are  readily  soluble  in 
lipoids,  and  yet  are  unable,  or  practically  unable,  to 
enter  the  living  cell;  while,  on  the  other  hand,  there 
are  dyes  for  which  the  plasmatic  membrane  is  highly 
permeable,  which,  however,  are  almost  insoluble  in  chole- 
sterol. Some  workers  contend  that  the  plasmatic  mem- 
brane is  protein,  rather  than  lipoid,  in  character.3 

The  statement  that  simple  inorganic  salts  are  unable 
to  penetrate  the  protoplasmic  membrane  is  not  absolutely 
correct.  The  very  fact  that  the  cell  sap  contains  salts 

1  Lanolin,  for  instance,  which  is  obtained  from  wool  oil,  and  con- 
tains appreciable  quantities  of  cholesterol,  takes  up  in  the  anhydrous 
state  about  an  equal  weight  of  water. 

2  Jahrb.  wiss.  Bot.,  1908,  46,  1. 

3  See  Robertson,  /.  Biol.   Chem.,  1908,  4,  1 ;   Osterhout,  The  Plant 
World,  1913,  16,  129. 


84  PHYSICAL  CHEMISTRY 

which  are  supplied  to  the  plant  in  the  nutrient  medium 
in  which  it  grows  indicates  that  there  must  be  provision 
of  some  kind  for  the  absorption  of  these  salts.  Further, 
a  direct  proof  of  the  penetration  of  some  inorganic  salts 
into  living  protoplasm  has  recently  been  described  by 
Osterhout.1  His  experiments  were  carried  out  chiefly 
with  Dianthus  barbatus,  which  can  be  grown  in  distilled 
water,  and  the  root  hairs  of  which  during  such  growth 
remain  free  from  calcium  oxalate  crystals.  When, 
however,  they  are  transferred  from  distilled  water  to  a 
dilute  solution  of  a  calcium  salt,  the  presence  of  calcium 
oxalate  crystals  in  the  root  hairs  is  evident  within  a 
few  hours.  This  shows  that  calcium  salts  may  penetrate 
fairly  rapidly  into  living  protoplasm.  The  subsequent 
growth  is  normal,  so  that  the  penetration  of  the  calcium 
salts  is  not  due  to  any  abnormal  or  injured  condition 
of  the  cells. 

Difficulties  of  a  Purely  Physical  Theory  of  Per- 
meability.— It  must  be  recognised  that  the  behaviour 
of  the  living  cell  membrane  towards  the  substances  with 
which  it  comes  in  contact  is  in  many  cases  incapable 
of  interpretation  on  a  purely  physical  basis.  Although 
this  is  not  the  place  for  a  discussion  of  the  problem 
of  permeability  in  its  physiological  aspect,  it  is  worth 
while  to  indicate  one  or  two  of  the  facts  in  the  face 
of  which  any  purely  physical  theory  is  found  wantmg. 
It  is  well  known,  for  instance,  that  the  permeability 
of  a  cell  membrane  alters  on  the  death  of  the  cell ; 
certain  ^dyes  carf  enter  the  cell  only  when  the  latter 
is  killed^  Again,  there  is  the  very  striking  fact  that  the 
inojzganicHJSonstituents  of  the  blood  corpuscle  are  notably 
different  from  those  of  the  plasma:  the  corpuscle  fluid 
is  comparatively  rich  in  potassium  and  phosphate,  while 
the  plasma  is  poor  in  these,  but  rich  in  sodium  and 


PERMEABILITY  AND  IMPERMEABILITY    85 

chloride.  From  the  fact  that  the  cell  receives  its  nutri- 
ment from  the  external  medium,  it  appears  that  the  mem- 
brane cannot  be  absolutely  impermeable  to  potassium  salts, 
and  yet  their  retention  in  the  cell  would  seem  to  be  im- 
possible if  permeability  of  the  membrane  is  conceded.  We 
are  therefore  driven  to  assume  some  specific  intervention 
of  the  living  membrane  or  some  special  affinity  between 
the  cell  protoplasm  and  the  potassium  salts.1 

There  are  cases  also  where  the  membrane  surrounding 
an  organ,  or  even  a  whole  organism,  behaves  in  a  way 
which  is  incompatible  with  a  purely  physical  theory  of 
permeability  and  osmosis.  In  the  processes  of  secretion 
it  is  found  that  owing  to  the  specific  activity  of  the 
secretory  organs  a  substance  may  be  transferred  from 
a  place  where  its  concentration  is  low  to  a  place  where 
its  concentration  is  high.  In  the  kidneys,  for  instance, 
urea  is  transferred  from  the  blood,  which  contains  little 
of  it,  to  the  urine,  in  which  the  proportion  of  urea  is 
much  greater.  This  could  not  be  effected  by  any  purely 
osmotic  agency.  Reference  may  be  made  also  to  some 
interesting  observations  on  tadpoles  made  by  Overton. 
Immersed  in  a  5—6  per  cent,  sucrose  solution  or  in  a 
0'6  per  cent,  sodium  chloride  solution,  tadpoles  are  un- 
affected, and  their  activity  is  unimpaired.  If  they  are 
transferred  to  an  8  per  cent,  sucrose  solution  or  an  0*8 
per  cent,  sodium  chloride  solution,  they  lose  a  consider- 
able quantity  of  water  in  the  course  of  twenty-four  hcoirs, 
and  shrink  notably  in  size.  A  similar  result  is  produced 
by  immersion  of  the  tadpoles  in  solutions  of  uninjurious 
substances  which  are  hypertonic  to  a  6  per  cent,  sucrose 
solution.  Immersion  in  a  solution  hypotonic  to  a  6  per 
cent,  sucrose  solution  we  should  expect  to  be  followed 
by  an  intake  of  water,  and  consequent  increase  in  the 
size  of  the  tadpoles.  This  however  is  not  the  case,  and 

1  See  Moore  and  Koaf,  Biochem.  J.t  1908,  3,  55  ;  1911,  6,  110. 


Boa         ;  '       PHYSICAL  CHEMISTRY 

it  therefore  appears  that  the  epithelial  membranes  of  the 
tadpole  are  permeable  J}O  water  in  the  one  direction, 
but  not  in  the  other.  This  fact,  and  the  others  which 
have  just  been  quoted,  will  serve  to  show  that  a  purely 
physical  theory  of  the  exchanges  which  take  place  across 
a  living  membrane  is  inadequate ;  there  is  a  physiological 
permeability  as  well  as  a  physical  permeability. 

Permeability  and  Surface  Tension  of  the  Cell  Mem- 
brane.— As  indicated  by  the  phenomena  of  plasmolysis, 
the  pla^roatic  membrane  of  plant  cells  is  normally  im- 
permeable to  the  suiiafcajicfis__presejit-  in  the  cell  sap. 
There  are  conditions,  however,  in  which  the  membrane 
loses  its  power  of  retaining  these  substances,  and  the 
manner  in  which  this  may  be  brought  about  artificially 
is  of  great  interest  and  importance.  The  researches  of 
Czapek1  have  shown  that,  as  a  convenient  test  for  the 
unimpaired  character  of  the  cell  membrane,  the  reaction 
between  tannin  and  caffeine  (cp.  p.  81)  may  be  employed. 
In  a  very  large  number  of  cases  tannin  is  a  constituent 
of  the  cell  sap,  and  so  long  as  the  impermeability  of  the 
protoplasmic  membrane  is  intact,  immersion  of  such  cells 
in  a  dilute  caffeine  solution  will  lead  to  the  formation  of 
a  precipitate  inside  the  cell.  If,  on  the  other  hand,  the 
cells  have  been  exposed  to  such  conditions  as  destroy  the 
impermeability  of  the  membrane,  then  the  tannin  will 
diffuse  away,  and  after  a  time  the  reaction  with  caffeine 
will  be  very  feeble,  if  not  entirely  absent. 

In  his  systematic  study  of  the  effect  of  different  sub- 
stances (in  aqueous  solution)  on  the  permeability  of 
higher  plant  cells,  Czapek  found  that  for  each  substance 
there  was  a  critical  concentration,  such  that  the  imper- 
meability of  the  cells  was  retained  if  they  were  immersed 

1  Ueber  eine  Meihode  zur  direkten  Bestiminung  der  Oberflachenspannung 
der  Plasmahaut  von  Pflanzenzellen  (Gustav  Fischer  ;  Jena,  1911). 


PERMEABILITY  AND  IMPERMEABILITY    855 

for  some  time  in  a  weaker  solution,  but  rapidly  destroyed 
if  they  were  immersed  in  a  stronger  solution.  In  the 
series  of  the  fatty  alcohols,  for  instance,  these  critical 
concentrations  are  about  14  per  cent,  by  weight  for 
methyl  alcohol,  8-9  per  cent,  for  ethyl  alcohol,  4  per  cent, 
for  71-propyl  alcohol,  To  per  cent,  for  n- butyl  alcohol,  and 
0*5  per  cent,  for  amyl  alcohol. 

Now  the  very  significant  fact  has  been  established 
that  all  these  critical  solutions  critical,  that  is,  for  the 
impermeability  of  the  cell  membrane — have  practically 
the  same  surface  tension,  the  average  value  being  0'685 
that  of  water.  The  conclusion  may  therefore  be  drawn 
that  this  figure  represents  the  natural  surface  tension  of 
the  plasmatic  membrane,  and  that  the  abnormal  permea- 
bility exhibited  by  higher  plant  cells  after  immersion  in 
solutions  above  the  critical  concentration,  results  from 
the  displacement  of  those  substances  which  are  normal 
constituents  of  the  membrane.  Further,  the  significant 
observation  has  been  made  that  the  surface  tension  of 
the  saturated  emulsions  of  neutral  fats  (containing 
notably  the  glycerides  of  unsaturated  fatty  acids)  has 
a  minimum  value  of  0'68  relatively  to  water.  The 
coincidence  of  this  figure  with  that  for  the  natural 
surface  tension  of  the  plasmatic  membrane  is  suggestive 
in  connection  with  the  question  as  to  the  nature  of  this 
membrane.  Attention  may  be  drawn  also  to  the  fact 
that  the  power  of  substances,  notably  the  fatty  alcohols, 
to  lower  the  surface  tension  of  water  stands  in  evident 
relationship  to  their  physiological  activity1  and  to  their 
haBmolytic  power.2 

1  Traube,  Ber.  deutsch.  physikal.  Oes.,  1904,  6,  326. 

2  Fiihner  and  Neubauer,  Archiv  exper.  PathoL,  1907,  56;  333. 


CHAPTER   VI 

VAPOUR    PRESSUKE,    BOILING    POINT    AND    FREEZING 
POINT   OF   SOLUTIONS 

Vapour  Pressure  of  Solvent  and  Solution. — The  direct 
determination  of  the  osmotic  pressure  of  a  solution  is 
no  easy  matter.  There  are  however  other  properties  of 
solutions  which  are  quantitatively  related  to  osmotic 


Temperature 


FIG.  7. 


pressure,  and  serve  therefore  for  its  indirect  evaluation. 
The  first  of  these  is  the  vapour  pressure.  Investigation, 
chiefly  by  Raoult,  has  shown  that  when  the  dissolved 
substance  is  non-volatile  the  vapour  pressure  of  a  dilute 


VAPOUR  PRESSURE 


87 


solution  is  lower  than  that  of  the  pure  solvent  at  the  same 
temperature  by  an  amount  which  is  proportional  to  the 
concentration  of  the  dissolved  substance.  The  general 
relation  between  the  vapour  pressure  of  the  solvent 
and  that  of  the  solution  at  different  temperatures  is 
represented  by  the  curves  in  Fig.  7,  the  upper  curve 
showing  the  variation  in  the  vapour  pressure  of  the 
solvent  with  rising  temperature,  the  lower  curve  showing 

the  corresponding  variation 
in  the  vapour  pressure  of 
the  solution.  The  relative 
position  of  the  two  curves 
is  such  that,  if  AC  and  BO 
represent  the  vapour  pres- 
sures of  solvent  and  solution 
at  one  temperature,  A'C'  and 
B'C'  the  same  quantities 
at  any  other  temperature, 
BC  B'C'  ' 


V//////////////A 


simply  that  for  a  given  solu- 
tion the  ratio  of  the  vapour 
pressures  of  solution  and 
solvent  is  the  same  at  all 
temperatures. 

Vapour     Pressure     and 
Osmotic      Pressure.  —  The 

mere  fact  of  the  existence 
of  osmotic  pressure  involves 

the  consequence  that  the  solution  of  a  non-  volatile  substance 
must  have  a  lower  vapour  pressure  than  the  solvent 
at  the  same  temperature.  The  connection  between  the 
two  will  be  made  evident  by  consideration  of  Fig.  8. 
Suppose  that  A  is  a  funnel  and  tube  closed  at  the  bottom 
by  a  semi  -permeable  membrane,  and  containing  sucrose 


FIG.  8. 


88  PHYSICAL   CHEMISTRY 

solution.  Suppose  also  that  osmotic  equilibrium  has 
been  established  between  the  sucrose  solution  and  the 
pure  water  in  the  vessel  B,  that,  in  fact,  the  weight  of 
the  column  CD  is  equal  to  the  osmotic  pressure  of  the 
sucrose  solution.  If  the  whole  apparatus  stands  in  a 
vessel  from  which  the  air  has  been  removed,  the  space 
inside  the  vessel  will  be  occupied  by  water  vapour.  Now 
in  any  gaseous  atmosphere  the  density,  and  therefore  the 
pressure,  of  the  gas  is  greatest  at  the  bottom,  because 
there  the  weight  of  the  overlying  column  is  a  maximum  ; 
the  pressure  at  a  higher  point  is  less  in  proportion  as 
the  weight  of  the  gaseous  column  above  is  diminished. 
Hence  the  pressure  of  water  vapour  at  C,  level  with 
the  top  of  the  sucrose  solution  in  A,  is  less  than  at  D, 
the  surface  of  the  water.  The  pressure  at  D  is  the 
vapour  pressure  of  water  at  the  temperature  of  the 
apparatus,  and,  since  there  is  equilibrium,  the  pressure 
at  C  must  be  equal  to  the  vapour  pressure  of  the  sucrose 
solution,  the  surface  of  which  is  at  this  level;  that  is, 
the  vapour  pressure  of  a  solution  must  be  lower  than 
that  of  the  solvent  at  the  same  temperature.  Further, 
it  is  apparent  that  the  difference  between  the  vapour 
pressures  is  equal  to  the  weight  of  a  column  of  water 
vapour  of  height  equal  to  CD. 

When  the  relationship  between  the  osmotic  and  vapour 
pressures  of  a  solution  is  treated  mathematically,  it  is 


~, 

found  that  P—  -^-  •  loge  —,*  where  P  is  the  osmotic  pres- 


sure and  p'  the  vapour  pressure  of  the  solution  ;  p  is  the 
vapour  pressure,  M  the  molecular  weight,  and  S  the 
specific  gravity  of  the  solvent  ;  T  is  the  absolute  tem- 
perature, and  R  is  the  gas  constant.  A  glance  at  the 
formula  will  show  that  in  order  to  calculate  the  osmotic 
pressure  of  a  solution  from  its  vapour  pressure  it  is  not 
necessary  to  know  the  absolute  values  of  p  and  p'  ';  a 


VAPOUR   PRESSURE  89 

knowledge  of  the  ratio  of  the  vapour  pressure  of  the 
solvent  to  that  of  the  solution  is  sufficient.  It  is,  as 
a  matter  of  fact,  an  easier  matter  to  determine  the  ratio 
of  the  vapour  pressures  of  solvent  and  solution  than  to 
determine  their  absolute  values. 

One  very  simple  method  of  finding  the  ratio  in  question 
when  water  is  the  solvent  is  that  devised  by  Ostwald  and 
Walker.1  A  current  of  air  is  drawn  slowly  through  (1) 
Liebig's  bulbs  charged  with  the  aqueous  solution  under 
examination,  (2)  another  set  of  bulbs  similarly  charged, 
(3)  bulbs  containing  water,  (4)  a  U-tube  containing 
pumice  moistened  with  concentrated  sulphuric  acid. 
When  the  air  leaves  (2)  it  is  charged  with  water  vapour 
up  to  the  pressure  of  the  solution;  when  it  leaves  (3) 
it  is  charged  with  water  vapour  up  to  the  pressure  of 
pure  water  at  the  same  temperature.  The  air  therefore 
takes  up  water  during  its  passage  through  the  bulbs  (3), 
and  the  loss  of  weight  which  these  bulbs  show  is  pro- 
portional to  the  difference  p—p'.  In  passing  through 
the  sulphuric  acid  tube  the  air  is  deprived  of  the 
whole  of  the  water  vapour  which  it  has  taken  up,  and 
the  gain  in  weight  of  this  tube  during  an  experiment 
is  therefore  proportional  to  p.  A  determination  of  the 
loss  in  weight  of  (3),  and  the  gain  in  weight  of  (4), 
after  a  current  of  air  has  been  passed  for  some  time, 
gives  the  required  ratio  of  the  vapour  pressures,  for 

p-p'  _        loss  in  weight  of  water  bulbs  -,    -  ,  .     £ 

p     ~  gain  in  weight  of  sulphuric  acid  tube  '  p' 

can  be  easily  calculated.  Since,  as  already  stated,  the 
value  of  -,  is  independent  of  temperature,  it  is  not  essen- 
tial in  this  method  to  keep  the  temperature  absolutely 
constant  throughout  an  experiment ;  it  is  necessary  only 

1  Walker,  Zeit  physikal  Chem.,  1888,  2,  602. 


90  PHYSICAL  CHEMISTRY 

to  ensure  that  the  variation  of  temperature,  if  any,  shall 
be  the  same  for  all  parts  of  the  apparatus. 

This  method  of  finding  the  relative  vapour  pressures 
of  solvent  and  solution  has  lately  been  modified  and 
improved  by  Lord  Berkeley  and  Mr.  Hartley,1  who 
arranged  that  the  current  of  air,  instead  of  bubbling 
through  the  solvent  and  the  solution,  should  pass  over 
their  surfaces  in  specially  constructed  apparatus;  in 
this  way  equality  of  the  air  pressure  is  secured  through- 
out the  train  of  vessels.  In  order  to  ensure  rapid  and 
complete  saturation  of  the  air  with  water  vapour  the 
vessels  containing  the  solution  and  the  solvent  are 
regularly  rocked,  so  that  the  exposed  surface  of  liquid 
is  constantly  being  renewed.  With  this  apparatus  Lord 
Berkeley  and  Mr.  Hartley  have  determined  the  value 

of  -,  for  various  solutions  of  sucrose  and  calcium  ferro- 

cyanide,  the  osmotic  pressures  of  these  solutions  being  then 
calculated  from  the  vapour  pressure  ratio  by  a  formula 
similar  to  that  quoted  above.  It  is  interesting  to  com- 
pare the  values  thus  indirectly  obtained  for  the  osmotic 
pressure  of  calcium  ferrocyanide  solutions  with  those 
determined  by  the  direct  method  described  on  p.  50. 

Osmotic  Pressure  in  Atmospheres. 

Grams  Anhydrous  Salt  per  nv>e^  .,rQ^  Calculated  from 

100  grams  of  Water.  'ed-          Vapour  Pressure. 

31-39  41-22  41-24 

39-50  70-84  70-61 

42-89  87-09  86-61 

47-22  112-84  11296 

49-97  130-66  131-45 

Vapour  Pressure  and  Molecular  Weight.  —  Since* 
there  is  this  quantatitive  relationship  between  vapour 
pressure  and  osmotic  pressure,  and  since,  as  already 
shown,  a  knowledge  of  the  osmotic  pressure  of  a  solution- 

1  Proc.  Roy.  Soc.,  1906,  A,  77,  156  ;  Phil.  Trans,,  1909,  A,  209,  177. 


VAPOUR  PRESSURE  91 

permits  a  calculation  of  the  molecular  weight  of  the 
dissolved  substance,  there  must  be  some  way  of  de- 
ducing the  molecular  weight  directly  from  the  vapour 
pressure.  The  required  relationship  is  given  by  the 

formula  ?—¥-=  n™y,   where  p  and  yf   are   the   vapour 


pressures,  as  before,  of  solvent  and  solution,  n  is  the 
number  of  solute  molecules,  and  JV  is  the  number  of 
solvent  molcules  in  the  solution.  A  slight  transformation 


of  the  formula  gives    —-  =     ,  so  that  n  =  Nf-.     In 

order  to  illustrate  the  use  of  this  formula  the  following 
data  may  be  considered.  A  solution  of  11*35  grams  of 
oil  of  turpentine  in  100  grams  of  ether  was  found  to  have 
a  vapour  pressure  of  36  "01  cm.,  the  vapour  pressure  of 
pure  ether  at  the  same  temperature  being  38'3  cm.  The 
molecular  weight  of  ether  is  74,  so  that  the  value  of  N  for 

n    ,.        .     100         -,          100      38-3-36-01       ~oa 
the  given  solution  is  -^-,  and  n—-^  X  —  3Q.(ji  —  ='086  ; 

that  is,  1T35  grams  is  '086  of  a  gram-molecule,  and 
the  molecular  weight  of  oil  of  turpentine  is  there- 

1  1  »Qf^ 

fore   -^gg  =132,    in    agreement    with    the    theoretical 

value  136. 

A  glance  at  the  formula  connecting  osmotic  pressure 

D     SRT  ,        p      i 
and    vapour    pressure,    viz.    P  =  -^-  .  loge  —,  ,  shows  that 

when  solutions  of  two  non-volatile  substances  in  the 
same  solvent  have  the  same  vapour  pressure  at  any 
temperature,  their  osmotic  pressures  must  be  equal  ;  the 
solutions  are  isotonic.  Now  it  has  already  been  shown 
on  p.  62  that  if  we  can  find  isotonic  solutions  of  two 
substances,  the  molecular  weight  of  the  one  can  be 
deduced  from  that  of  the  other.  Hence  it  follows  that 
if  we  can  find  solutions  of  two  substances  which  have 
the  same  vapour  pressure,  the  molecular  weight  of  the 


92  PHYSICAL  CHEMISTRY 

second   can    be   calculated,    when  that   of    the  first    is 
taken  as  known. 

An  interesting  microscopic  method  of  finding  isotonic 
solutions,  and  therefore  also  of  determining  molecular 
weights,  has  been  described  by  Barger.1  During  some 
experiments  on  the  growth  of  fungi  in  concentrated 
solutions  it  had  been  noticed  that  when  a  drop  of 
strong  salt  solution  is  kept  for  some  time  in  a  small 
enclosed  space  in  which  water  also  is  present  the 
size  of  the  drop  gradually  increases.  This  is  obviously 
due  to  the  fact  that  the  vapour  pressure  of  the 
water  is  greater  than  that  of  the  salt  solution,  and 
hence  there  results  a  slow  distillation  from  the  water 
to  the  solution.  In  Barger's  method  a  solution  B  is 
made  up  of  the  substance  of  unknown  molecular  weight, 
as  well  as  a  number  of  solutions  Av  Az,  &c.,  of  a 
standard  substance  the  molecular  weight  of  which  is 
known ;  these  last  solutions  form  a  series  of  gradually 
increasing  concentration.  Alternate  drops  of  A^  and  E 
are  now  introduced  into  a  capillary  tube,  and  any 
variation  in  the  size  of  the  drops  is  observed  under 
the  microscope  from  time  to  time.  If  the  size  of  the 
B  drops  increases  at  the  expense  of  the  Al  drops,  it 
follows  that  the  vapour  pressure  of  B  is  less  than  the 
vapour  pressure  of  Av  and  therefore  that  the  osmotic 
pressure  of  B  is  greater  that  that  of  Ar  The  experiment 
is  now  repeated  with  the  whole  series  of  A  solutions, 
when  it  will  be  found  that  there  are  two  adjoining 
members  of  the  series  A±  and  A^  we  shall  suppose, 
such  that  when  alternate  drops  of  A±  and  B  are  put 
in  a  capillary  tube  the  B  drops  increase  in  size  at  the 
expense  of  the  A±  drops,  while  in  a  similar  experiment 
with  A5  and  B,  the  A5  drops  increase  at  the  expense 
of  the  B  drops.  The  solution  of  A  which  has  the 

1  Journ.  Chem.  Soc.,  1904,  85,  286. 


VAPOUR  PRESSURE  93 

same  vapour  pressure  and  the  same  osmotic  pressure 
as  B  must  therefore  lie  between  A±  and  A5.  The  appli- 
cation of  this  method  may  be  illustrated  by  the  following 
example.  Drops  of  an  alcoholic  solution  of  azobenzene 
containing  30*94  grams  per  litre  were  alternated  with 
drops  (1)  of  an  alcoholic  solution  containing  0*16  mole- 
cule a-naphthol  per  litre,  (2)  of  an  alcoholic  solution  of 
the  same  substance  containing  0'18  molecule  per  litre. 
In  the  first  case  the  drops  of  the  azobenzene  solution 
increased  in  size,  in  the  second  case  they  decreased. 
A  solution  of  azobenzene  containing  30*94  grams  per  litre 
is  therefore  isotonic  with  a  solution  containing  between 
0'16  and  0'18  molecule  of  a-naphthol  per  litre.  If  the 
azobenzene  solution  were  isotonic  with  the  weaker  of 
these  a-naphthol  solutions,  and  if  these  two  substances  are 
assumed  to  have  the  same  isotonic  coefficient,  then  the 

30*94  x  1 
molecular  weight  of  azobenzene  would  be  — ^ —  =  193. 

If,  on  the  other  hand,  the  azobenzene  solution  were 
isotonic  with  the  stronger  of  the  a-naphthol  solutions, 
then  the  molecular  weight  of  azobenzene  would  be 

—     x    =172.     The  conclusion,   therefore,   to   be  drawn 

*  lo 

from  this  experiment  is,  that  the  molecular  weight  of 
azobenzene  lies  between  172  and  193.  The  value  corre- 
sponding to  the  formula  for  azobenzene  is  182. 

In  some  ways  the  method  which  has  just  been  de- 
scribed recalls  the  hsematocrit  method  of  finding  isotonic 
solutions.  In  both  cases  transference  of  the  solvent  takes 
place  across  a  semi-permeable  membrane ;  in  Barger's 
arrangement,  provided  that  the  dissolved  substances  are 
non-volatile,  the  space  between  two  neighbouring  drops 
is  permeable  only  to  the  molecules  of  the  solvent,  and  is 
therefore  equivalent  to  a  semi-permeable  membrane. 

Osmotic   Pressure   and  Boiling   Point. — The  boiling 


94 


PHYSICAL   CHEMISTRY 


point  of  a  liquid  is  the  temperature  at  which  its  vapour 
pressure  is  equal  to  the  atmospheric  pressure.  Provided 
that  we  are  dealing  with  a  non-volatile  solute,  the  vapour 
pressure  curve  for  the  solution  lies  below  the  vapour 
pressure  curve  for  the  pure  solvent;  hence,  as  shown 
graphically  in  Fig.  9,  the  solution  must  be  raised  to  a 
higher  temperature  before  its  vapour  pressure  becomes 
equal  to  the  atmospheric  pressure;  that  is,  the  boiling 
point  of  the  solution  is  higher  than  that  of  the  solvent. 


760 
mm. 


Temperature  T0        T 

FIG.  9. 

Furtheivthe  rise  or  elevation  of  the  boiling  point,  T—  T0, 
is  quantitatively  related  to  the  lowering  of  the  vapour 
pressure,  and  therefore  also  to  the  osmotic  pressure.  The 
relation  between  the  osmotic  pressure  of  a  moderately 
dilute  solution  and  its  boiling  point  is  given  by  the 

1000S!/       T T 

formula  P=-^  — ™~ °  atmospheres,   where  S  is   the 

^4*zO  J  Q 

specific  gravity  of  the  solvent  at  its  boiling  point,  I  is 
the  latent  heat  of  vaporisation  for  1  gram  of  the  solvent, 


BOILING  POINT  96 

T0  is  its  boiling  point,  and  T  that  of  the  solution.  In 
the  case  of  an  aqueous  solution  $=  0*959,  /  =  536,  and 
T0  =  373,  so  that  the  osmotic  pressure  of  an  aqueous 
solution  which  boils  T—  T0  degrees  above  the  boiling 
point  of  water  is  56*8  (T—  T0)  atmospheres.  If  the 
solution  boils,  for  instance,  0*1°  higher  than  water,  its 
osmotic  pressure  is  5*68  atmospheres. 

Boiling  Point  and  Molecular  Weight. — In  view  of 
the  existence  of  a  quantitative  relationship  between  the 
osmotic  pressure  and  boiling  point  of  a  solution,  it  is 
obvious  that  there  must  be  a  definite  connection  also 
between  the  elevation  of  boiling  point  and  the  mole- 
cular weight  of  the  dissolved  substance.  The  nature 
of  this  connection  may  be  deduced  empirically  in  the 
following  way. 

Experiments  have  shown  that  the  extent  to  which 
the  boiling  point  of  a  given  solvent  is  raised  by  the 
addition  of  a  non-volatile  substance  is  proportional  to 
the  concentration  of  that  substance.  This  is  borne  out 
by  the  numbers  in  the  following  table,1  those  in  the 
first  column  representing  the  weights  of  phenanthrene 
dissolved  in  each  case  in  22'75  grams  of  benzene,  those 
in  the  second  column  giving  the  observed  rise  of  the 
boiling  point  above  that  of  pure  benzene ;  the  third 
column  contains  the  ratios  of  the  numbers  in  the  first 
and  second  columns : — 

Grams  Rise  of  T?OH« 

Phenanthrene.  Boiling  Point. 

0-619  0-389°  1-59 

1-018  0-639°  1-59 

1-648  1-023°  1-61 

From  these  data,  as  well  as  from  many  others  that 
might  be  quoted,  it  appears  that  the  value  of  the  ratio 
is  practically  constant,  and  we  may  therefore  conclude 

1  Biltz,  Die  Praxis  der  Molekelgewichtsbestimmung. 
'-  G 


96  PHYSICAL   CHEMISTRY 

that  the  rise  of  boiling  point  is  proportional  to  the  con- 
centration of  the  solute. 

Assuming  that  this  rule  is  valid  even  for  concentrated 
solutions,  we  may  easily  calculate  What  elevation  would 
be  observed  if  the  solution  under  examination  contained 
1  gram-mol.  of  phenanthrene  in  some  definite  quantity 
(say  100  grams)  of  benzene.  The  first  solution,  for 
instance,  quoted  in  the  above  table  contains  0*619  gram 
of  phenanthrene  in  22*75  grams  of  benzene;  this  is 

the  same  as  a  solution  containing  —        —  =  2'72  grams 

of  phenanthrene  per  100  grams  of  benzene.  If  this 
quantity  of  benzene  contained  a  gram-mol.  —  178  grams 
—  of  phenanthrene,  the  corresponding  elevation  would 

be  °'38297*178  =  25*50.     Suppose  now  another  set  of  data, 

relating  to  a  solution  of  phenyl  benzoate  in  benzene, 
is  similarly  treated.  A  solution  containing  1*015  gram  of 
phenyl  benzoate  in  33*38  grams  of  benzene  boils  0'387° 
higher  than  pure  benzene.  In  this  case  the  solution  is  the 

.    .    .        1-015  x  100      0  n/1  £     , 

same  as  one  containing  —  %&%%  —  =  3  '04  grams  of  phenyl 


benzoate  per  100  grams  of  benzene.  On  the  basis  of 
proportionality  between  rise  of  boiling  point  and  con- 
centration, the  elevation  calculated  for  a  solution  con- 
taining 1  gram-mol.  —  198  grams  —  of  phenyl  benzoate 


in    100   grams   of   benzene   would   be      —      —  =  25*2°. 


This  is  very  nearly  the  same  figure  as  that  calculated 
from  the  data  for  the  phenanthrene  solution,  and  in- 
stances of  similar  agreement  might  be  multiplied. 

It  is  found,  in  fact,  that  when  experimental  data 
for  the  boiling  points  of  benzene  solutions  are  used 
to  calculate  the  elevation  which  would  be  produced  by 
dissolving  1  gram-mol.  of  solute  in  1  00  grams  of  benzene, 
the  figures  obtained  in  the  majority  of  cases  lie  between 


BOILING  POINT  97 

25°  and  27°.  This  quantity  appears  therefore  to  be  a 
characteristic  constant  for  benzene,  independent  of  the 
particular  substance  which  is  employed  as  solute ;  it  is 
referred  to  as  the  'molecular  elevation  of  the  boiling 
point'  or  as  the  'boiling  point  constant.'  In  the  case 
of  benzene  the  figure  which  has  been  chosen  as  giving 
the  best  value  for  the  molecular  elevation  of  the  boil- 
ing point  is  26'7°.  When  the  experimental  data  for 
the  boiling  points  of  solutions  in  water,  alcohol,  chloro- 
form, &c.,  are  treated  in  the  same  way  as  has  been  done 
for  benzene,  there  is  similarly  obtained  in  each  case 
a  characteristic  constant ;  the  value  of  the  molecular 
elevation  of  the  boiling  point  (k)  is  5*2°  for  water, 
11-5°  for  ethyl  alcohol,  21'0°  for  ether,  and  39'(P  for 
chloroform. 

It  is  noteworthy  that  the  values  of  k  deduced  by  cal- 
culation from  the  experimental  data  can  be  confirmed. 

On  theoretical  grounds  k  = °_,  where  TQ  is  the  boiling 

point  of  the  solvent  on  the  absolute  scale,  and  /  is  its 
latent  heat  of  vaporisation.  The  values  of  k  calculated 
for  various  solvents  by  this  formula  are  in  good  agree- 
ment with  the  figures  quoted  above. 

When  a  trustworthy  value  has  been  obtained  for  k 
for  any  particular  solvent,  it  is  possible  to  determine 
the  molecular  weight  of  any  new  substance  in  this 
solvent.  Suppose  that  a  solution  of  g  grams  of  this 
substance  in  100  grams  of  the  solvent  is  found  to  boil 
t°  higher  than  the  pure  solvent ;  if  the  molecular  weight 
of  the  solute  is  M,  then  the  molecular  elevation  of  the 

boiling  point  will  be  —t,  and  this  must  be   equal  to  k, 

9  M 

which    is   already    known.      We    have    therefore    — t  =  k, 

7 

or  M=— '•/•  .     The  following  figures  illustrate  the  appli- 
t 


98  PHYSICAL  CHEMISTRY 

cation  of  this  formula.  A  solution  containing  0'939  gram 
of  a  certain  substance  in  30  grams  of  benzene  boils  0-588° 
higher  than  pure  benzene.  As  benzene  is  the  solvent, 
k  =  26 -7°;  g,  the  weight  of  solute  per  100  grams  of  the 
S0lvent,  =^?9X_00  =  3.13;  sothat  Jf=?6^13=142 

Practical  Determination  of  the  Rise  of  Boiling 
Point.  Beckmann's  Method. — A  thermometer  registers 
the  same  temperature  when  surrounded  by  the  steam 
from  boiling  water  as  it  does  when  surrounded  by  the 
steam  from  a  boiling  sugar  or  salt  solution.  In  order 
therefore  to  find  the  rise  of  boiling  point  for  such  a 
solution,  the  bulb  of  the  thermometer  must  be  immersed 
(1)  in  boiling  water,  (2)  in  the  solution  boiling  under 
the  same  conditions.  A  similar  statement,  naturally, 
applies  to  other  solvents  than  water.  It  is  found, 
however,  that  a  thermometer  immersed  in  a  boiling 
liquid  will  register  slightly  different  temperatures  accord- 
ing to  the  way  in  which  the  heat  is  applied  and  the 
rate  at  which  it  is  boiled.  If  the  boiling  vessel  is  in 
direct  contact  with  a  flame  it  is  hardly  possible  to 
avoid  superheating,  and  this  leads  to  oscillation  in  the 
readings  of  the  thermometer.  Beckmann's  apparatus, 
which  is  commonly  used  in  determining  the  rise  of 
boiling  point,  is  designed  to  minimise  these  irregularities 
and  to  permit  the  comparison  of  solvent  and  solution 
under  the  same  conditions. 

One  form  of  Beckmann's  boiling  point  apparatus  is 
represented  in  Fig.  10.  The  boiling  tube  A  is  provided 
with  two  side  tubes  ^  and  t2,  the  former  serving  for 
the  introduction  of  material  into  the  boiling  tube,  the 
latter  holding  a  condenser  K.  The  lower  end  of  A  rests 
in  a  hole  cut  in  the  asbestos  sheet  L,  which  in  its  turn 
lies  on  the  sheet  of  wire  gauze  D^  The  short  glass  cylinder 
G  serves  as  an  air  jacket  for  A,  and  is  covered  with  a 


BOILING  POINT  99 

sheet  of  mica  S.     The  upper  end  of  the  tube  A  is  closed 


FIG.  10. 


by  a  stopper,  which  carries  the  Beckmarm  thermometer. 


100  PHYSICAL   CHEMISTEY 

When  an  experiment  is  to  be  made,  the  weight  of 
the  empty  dry  boiling  tube  is  first  ascertained.  Enough 
solvent  to  cover  the  bulb  of  the  thermometer  is  then 
introduced,  and  the  tube  is  weighed  again ;  the  difference 
between  the  two  weighings  gives  the  weight  of  solvent 
taken.  The  apparatus  is  then  set  up,  and  the  tube  is 
heated  by  a  small  Bunsen  flame.  In  order  to  ensure 
regular  ebullition,  and  so  avoid  oscillations  of  temperature 
as  far  as  possible,  it  is  advisable  to  put  some  glass  beads, 
garnets,  or  platinum  foil  in  the  boiling  tube.  According 
to  Beckmann,  platinum  foil  is  most  effective  in  promoting 
regular  boiling,  and  he  advises  the  use  of  10-20  grams 
of  platinum  foil  rolled  up  and  cut  so  as  to  form  small 
tetrahedra.  The  flame  must  be  so  adjusted  that  the 
liquid  in  the  tube  A  boils  freely ;  after  it  has  boiled 
for  15-20  minutes  the  temperature  ought  to  be  practi- 
cally constant,  and  readings  of  the  thermometer  made 
at  minute  intervals  ought  not  to  differ  from  a  mean 
value  by  more  than  0'01°.  The  constant  temperature 
thus  reached  is  taken  as  the  boiling  point  of  the  solvent. 

The  burner  is  then  put*  on  one  side,  and  after  the 
apparatus  has  cooled  a  little,  a  weighed  quantity  of  the 
solute  is  introduced  into  the  boiling  tube.  If  the  solute 
is  a  solid  substance,  it  is  best  to  introduce  it  in  the 
form  of  lumps,  or  pastilles  made  in  a  steel  press;  if 
the  solute  is  liquid,  a  pipette  shaped  like  a  Sprengel 
pyknometer  is  employed.  When  the  solute  has  been 
added,  the  burner  is  replaced  under  the  boiling  tube, 
the  size  of  flame  remaining  unaltered.  The  solution  is 
now  boiled  until  a  steady  temperature  is  attained;  the 
reading  of  the  thermometer  then  recorded  is  taken  as 
the  boiling  point  of  the  solution.  A  fresh  addition  of 
solute  may  be  made,  and  the  corresponding  boiling  point 
determined  in  a  similar  manner.  ^  Since  the  boiling  point 
of  a  liquid  varies  notably  with  the  atmospheric  pressure, 


BOILING;  POINT ;  :;';  ';,>;;•',,•  I  $1 

it  is  advisable  to  complete  such  a  series  of  experiments  in 
as  short  a  time  as  possible. 

The  Beckmann  Thermometer.— In  a  determination 
of  the  elevation  of  the  boiling  point  it  is  not  necessary 
to  know  the  actual  temperatures  at  which  solvent  and 
solution  boil ;  it  is  sufficient  to  know  accurately  the 
difference  in  their  boiling  points.  There  is  ^ 
therefore  no  objection  to  varying  the  quantity 
of  mercury  in  the  working  part  of  the  ther- 
mometer, and  thereby  adapting  it  for  use  with 
solvents  of  widely  different  boiling  points : 
the  scale  may  then  be  made  very  open  with- 
out the  instrument  becoming  inconveniently 
large.  In  the  Beckmann  thermometer,  which 
is  commonly  used  for  determining  the  rise 
of  boiling  point  and  depression  of  the  freezing 
point,  the  tube  is  sealed  at  the  bottom 
to  a  large  bulb,  and  at  the  top  to  a  reservoir 
in  which  any  excess  of  mercury  is  kept. 
The  scale  of  the  instrument  covers  a  range 
of  about  6°  Centigrade ;  the  length  corre- 
sponding to  each  degree  is  3-5  cm.,  and 
each  degree  is  divided  into  hundredths. 
The  form  of  the  reservoir  will  be  under- 
stood by  reference  to  the  accompanying 
diagram  of  the  thermometer  head  (Fig.  11). 

When  it  is  desired  to  alter  the  adjustment  of  the  thermo- 
meter, the  bulb  is  warmed  so  that  the  mercury  expands  a 
little  way  into  the  reservoir,  as  shown  in  the  diagram.  The 
mercury  at  the  top  of  the  reservoir  may  then  be  detached 
by  tapping,  so  that  the  thermometer  is  now  adjusted  for 
a  higher  temperature  than  previously;  or  mercury  may 
be  jerked  up  from  the  bottom  of  the  reservoir,  so  that 
the  thermometer  is  adjusted  for  a  lower  temperature. 


FIG.  11. 


i($  PJSYSICAL  .  CHEMISTRY 

Landsberger's  Apparatus  for  Determining  Rise  of 
Boiling  Point. — When  a  liquid  is  boiled  by  direct  contact 
with  a  flame,  superheating  to  some  extent  is  inevitable. 
In  order  to  avoid  this  difficulty  Landsberger  suggested 
that  a  solution  should  be  brought  to  its  boiling  point 
by  passing  in  the  vapour  of  the  solvent.  The  vapour 
pressure  of  the  solution,  it  must  be  remembered,  is  lower 
than  that  of  the  solvent  at  the  same  temperature,  so 
that,  for  instance,  when  steam  at  100°  is  passed  into  a 
salt  solution  at  100°  the  steam  condenses,  and  by  its 
latent  heat  of  vaporisation  raises  the  temperature  of  the 
salt  solution  above  100°,  ultimately  bringing  it  to  its 
boiling  point.  In  this  case  all  risk  of  superheating  is 
avoided,  by  virtue  of  the  remarkable  fact  that  the  heating 
agent  is  at  a  lower  temperature  than  the  solution  which 
is  being  boiled. 

In  Walker  and  Lumsden's  modification  of  Lands- 
berger's apparatus  (see  Fig.  12)  the  graduated  boiling 
tube  N  is  first  charged  with  a  small  quantity  of  solvent, 
and  this  is  boiled  by  passing  in  vapour  through  the 
tubes  B  and  R  from  the  flask  F,  where  a  large  quantity 
of  the  solvent  is  boiled  by  direct  heating.  When  the 
solvent  in  N  is  boiling  the  excess  of  vapour  escapes 
through  the  small  hole  H,  fills  the  space  between  the 
tubes  N  and  E,  and  finally  passes  out  into  the  con- 
denser C.  When  the  condensed  solvent  is  dropping 
regularly  from  the  end  of  the  condenser  the  thermometer 
T  is  read,  and  the  reading  gives  the  boiling  point  of  the 
solvent.  The  current  of  vapour  is  now  stopped,  and 
the  most  of  the  solvent  which  has  condensed  in  N  is 
poured  back  into  F.  A  weighed  quantity  of  the  solute 
is  introduced  into  N,  and  the  current  of  vapour  is  re- 
started;  when  the  solution  is  in  active  ebullition,  and 
the  condensed  solvent  is  dropping  from  the  end  of  the 
condenser  at  about  the  same  rate  as  before,  the  ther- 


BOILING  POINT 


103 


mometer  is  read,  and  the  current  of  vapour  is  stopped 
immediately.  The  thermometer  T  and  the  delivery  tube 
R  are  removed,  and  the  volume  of  solution  in  N  ascer- 
tained as  rapidly  as  possible.  The  boiling  points  of 


FIG.  12. 

solvent  and  solution  have  thus  been  determined  under 
the  same  conditions,  and  as  the  composition  of  the 
solution  is  known,  all  the  data  necessary  for  the  calcula- 
tion of  the  molecular  weight  are  available.1 

1   For  more  details  of  this  method,  see  Journ.  Chem.  Soc.,  1898,  73, 
502 ;  also  Turner,  ibid.,  1910,  97,  1184. 


104 


PHYSICAL   CHEMISTRY 


Osmotic  Pressure  and  Freezing  Point. — It  is  a  well- 
known  fact  that  the  freezing  point  of  a  solution  is  in 
all  ordinary  instances  lower  than  that  of  the  pure  solvent. 
That  such  must  be  the  case  can  be  shown  by  a  con- 
sideration of  the  relative  positions  of  the  vapour  pressure 
curves  for  solvent  and  solution ;  it  is  only  necessary  to 
take  into  account  also  the  existence  of  a  vapour  pressure 
curve  for  the  solid  solvent.  Below  the  freezing  point 
the  solid  solvent  has  a  tendency  to  pass  into  the  state 
of  vapour,  and  the  measure  of  this  tendency  at  each 


T  TQ  Temperature 

FIG.  13. 

temperature  is  the  vapour  tension  or  vapour  pressure. 
The  vapour  pressure  curve  for  the  solid  is  not  a  mere 
continuation  of  the  vapour  pressure  curve  for  the  liquid ; 
the  two  are  independent,  as  shown  at  F0S  and  F0L  in 
Fig.  13.  At  the  freezing  point,  however,  the  vapour 
pressures  of  solid  and  liquid  must  be  equal,  since  that  is 
the  temperature  at  which  the  two  are  in  equilibrium.  The 
two  curves  must  therefore  intersect  at  the  freezing  point, 
and  we  may  define  the  freezing  point  as  the  temperature 
at  which  the  vapour  pressure  curve  for  the  liquid  inter- 
sects the  vapour  pressure  curve  for  ^he  solid.  Similarly, 
the  freezing  point  of  a  solution  is  the  temperature  at 


FKEEZING   POINT  105 

which  the  vapour  pressure  curve  for  the  solution  cuts 
the  vapour  pressure  curve  for  the  solid  solvent,  and 
it  appears  from  the  relative  position  of  the  curves,  as 
shown  in  Fig.  13,  "that  F,  the  freezing  point  of  the 
solution,  must  be  at  a  lower  temperature  than  F0,  the 
freezing  point  of  the  pure  solvent. 

This  argument  assumes  that  when  a  solution  freezes 
it  is  pure  solid  solvent  which  crystallises  out.  This 
assumption  is  justified  in  the  great  majority  of  cases, 
and  for  aqueous  salt  solutions  it  can  easily  be  shown 
that  when  freezing  takes  place  pure  ice  separates  out.  A 

N 
test-tube  containing  ^^KMn04  is  kept  in  a  freezing 

mixture  for  a  short  time  until  the  layer  next  the  glass 
has  frozen  ;  the  tube  is  then  set  in  a  wider  jacket 
tube  and  again  immersed  in  the  freezing  mixture  ;  in 
this  way  the  freezing  of  the  permanganate  solution 
proceeds  more  slowly.  When  the  contents  of  the  tube 
have  solidified  completely  it  is  seen  that  the  coloured 
salt  has  been  concentrated  in  the  centre  of  the  test- 
tube,  and  is  surrounded  by  an  envelope  of  perfectly 
colourless  ice. 

The  extent  to  which  the  freezing  point  of  a  solution 
is  lower  than  that  of  the  solvent,  the  depression  of  the 
freezing  point,  as  it  is  called,  depends  then  on  the 
vapour  pressure  of  the  solution,  and  must  therefore 
be  quantitatively  related  to  the  osmotic  pressure.  The 
relation  between  osmotic  pressure  P  and  freezing  point 

,      ,,      j.          ,     „     lOOO&a    Tn—  T    ,  i 

is  given  by  the  formula  P—  24.25    •  -^  —  atmos.,  where 

S  is  the  specific  gravity,  T0  the  freezing  point,  and  co 
the  latent  heat  of  fusion  of  the  solvent,  while  T  is  the 
freezing  point  of  the  solution.  If  the  solvent  is  water, 

then  S=l,  w  =  79-6,  and  ro  =  273,  and 


that    the   osmotic   pressure   of    an   aqueous   solution    is 


106  PHYSICAL  CHEMISTRY 

given  by  the  formula  P=12'03(ro  -  T)  atmos.  The 
mean  value,  for  instance,  which  has  been  found  by 
various  investigators  for  the  freezing  point  of  a  1  per 
cent,  sucrose  solution  is  -0*0546°.  The  osmotic  pressure 
of  this  sucrose  solution  at  0°  C.,  calculated  by  the  fore- 
going formula,  would  therefore  be  Of656  atmosphere,  in 
good  agreement  with  the  value  (0'649)  found  by  Pfeffer. 

Freezing  Point  and  Molecular  Weight. — The  relation- 
ship existing  between  the  freezing  point  of  a  solution 
and  its  osmotic  pressure  involves  another  between  the 
freezing  point  and  the  molecular  weight  of  the  dissolved 
substance.  What  there  is  to  be  said  in  this  connection 
is  very  similar  to  what  has  already  been  said  about 
the  boiling  point ;  elevation  of  the  boiling  point  and  de- 
pression of  the  freezing  point  are  comparable  quantities. 

The  depression  of  the  freezing  point  for  a  solution 
is  proportional  to  the  concentration  of  the  dissolved 
substance.  This  statement  embodies  the  results  of  count- 
less observations,  and  may  be  illustrated  by  the  following 
data  for  the  depression  of  the  freezing  point  in  aqueous 
solutions  of  chloral  hydrate : — 

Grams  Chloral  Hydrate  Depression  of 

in  100  grams  Water.  Freezing  Point.  Ratio. 

2-834  0-335°  8'4 

4-878  0-575°  8-5 

6-595  0-775°  8'5 

If  on  the  basis  of  proportionality  between  freezing 
point  depression  and  concentration  we  calculate  what 
would  be  the  depression  for  a  solution  containing  1  gram- 
mol.  (165*5  grams)  of  chloral  hydrate  per  100  grams 
of  water,  we  obtain  for  the  three  solutions  quoted  the 
values  19-6°,  19-5°,  19-4°  respectively.  If  the  experi- 
mental data  for  solutions  of  other  non-electrolytes  in 
water  are  similarly  treated,  the  value  found  for  the 
depression  which  would  be  produced  by  1  gram-mol. 


FREEZING  POINT  107 

of  solute  in  100  grams  of  water  is  not  very  different 
from  the  figures  just  quoted.  A  solution,  for  instance, 
containing  0'609  gram  of  ethyl  alcohol  in  100  grams  of 
water  freezes  at  —  0'243°;  the  depression  for  a  gram- 

mol.   would   be   °'2A4jLx46==18-4°.      It   appears   therefore 
^  u  D\/y 

that  the  figure  for  the  depression  due  to  1  gram-mol. 
of  solute  in  100  grams  of  solvent  is  a  characteristic 
constant  for  each  solvent,  and  it  is  described  as  the 
'  molecular  depression  of  the  freezing  point,'  or,  shortly, 
as  the  'freezing  point  constant.'  The  accepted  value 
of  this  constant  (k)  for  water  is  18*6°,  for  acetic  acid 
39*0°,  and  for  benzene  50-0°.  On  theoretical  grounds 


k  =  _  °  ,  where  T0  is  the  freezing  point  of  the  solvent 

eo 

on  the  absolute  scale,  and  o>  is  the  latent  heat  of  fusion. 
It  is  interesting  to  note  that  the  values  thus  calculated 
for  k  are  in  good  agreement  with  those  deduced  from 
the  consideration  of  the  observed  depressions. 

The  value  of  k  which  has  been  adopted  for  any  solvent 
after  a  study  of  various  solutes  of  known  molecular  weight 
may  be  employed  in  determining  the  molecular  weight 
of  a  new  substance.  Suppose  that  for  a  solution  of  this 
new  substance  containing  g  grams  per  100  grams  of  solvent 
the  observed  depression  of  freezing  point  is  t°  ;  if  the 
required  molecular  weight  of  the  solute  is  M,  then  the 

TUT 

molecular  depression  of  the  freezing  point  would  be  —t, 

o 

and  this  must  be  equal  to  k,  which  is  already  known  ; 

that  is,  —  t  =  k,  or  M  —  —  —  -.     An  illustration  of  the  appli- 

9  * 

cation  of  this  formula  may  be  quoted.     A  solution  con- 

taining 0'565  of  a  certain  substance  in  23'4  grams  of 
water  freezes  at  —  0*77°  ;  it  is  required  to  calculate  the 
molecular  weight  of  this  substance.  The  value  of  g  in  this 


108 


PHYSICAL   CHEMISTRY 


case  is  °'56:1X1QQ  =  2-415,  and  since  k  for  water  =18-6°, 


M= 


23-4 
18-6X2-415 

0-77 


58-3. 


Experimental  Determination  of  the  Depression  of 
the  Freezing  Point. — The  ap- 
paratus chiefly  employed  for  this 
purpose  was  devised  by  Beckmann, 
and  is  represented  in  Fig.  14.  It 
consists  of  a  tube  A,  set  in  a 
jacket  tube  B,  and  provided  with 
a  Beckmann  thermometer  D,  and 
a  platinum  or  nickel  wire  stirrer. 
The  jacket  tube  B  rests  in  a 
metal  plate,  which  forms  the  cover 
of  the  thick  glass  jar  C.  When 
an  experiment  is  to  be  made  the 
glass  jar  is  filled  with  a  suitable 
cooling  mixture ;  the  mixture 
should  be  such  that  its  tempera- 
ture is  not  more  than  2°— 3°  below 

01  dJllJLsr^  ^)  ^e  freezing  point  of  the  solvent 
I  ^ — mfjff  — ^  *°  ^e  usec^  ^  known  weight  of 
solvent  is  put  in  the  tube  A,  and 
the  cork  carrying  thermometer 
and  stirrer  is  inserted ;  the  ther- 
mometer has  been  previously 
adjusted,  so  that  at  the  freezing 
point  of  the  solvent  the  top  of 
the  mercury  thread  is  somewhere 
on  the  upper  part  of  the  scale. 
The  tube  A  is  first  immersed 
directly  in  the  cooling  mixture, 
and  only  when  the  temperature  has 
fallen  nearly  to  the  freezing  point 
of  the  solvent  is  it  set  inside  the  jacket  tube.  The  contents 


FIG.  14. 


FBEEZING   POINT  109 

of  A  are  stirred  regularly,  and  the  temperature  falls  steadily. 
Close  observation  of  the  thermometer  shows  that  after 
a  short  time  the  mercury  ceases  to  fall,  then  rises  and 
remains  steady  at  one  point ;  the  temperature  thus 
marked  is  the  freezing  point  of  the  solvent.  The  tube 
A  is  now  taken  out  of  the  bath  and  a  weighed  quantity 
of  solute  is  introduced  through  the  side  tube;  after  it 
has  completely  dissolved,  the  operation  of  taking  the 
freezing  point  is  carried  out  as  before.  The  amount 
of  supercooling,  that  is,  the  interval  of  temperature  be- 
tween the  lowrest  point  to  which  the  mercury  falls  and 
the  highest  point  to  which  it  rises  (the  freezing  point, 
in  other  words),  should  be  noted ;  if  it  is  greater  than 
0'4°-0-50,  the  determination  of  the  freezing  point  should 
be  repeated,  and  the  occurrence  of  excessive  supercooling 
avoided  by  introducing,  if  necessary,  a  tiny  crystal  of 
the  solvent.  Excessive  supercooling  involves  the  separa- 
tion of  a  considerable  quantity  of  the  solid  solvent  when 
freezing  occurs,  and  this  would  mean  an  appreciable 
increase  in  the  concentration  of  the  solution.  When 
the  freezing  point  of  the  first  solution  has  been  satis- 
factorily determined,  a  further  quantity  of  solute  may 
be  introduced,  and  the  new  freezing  point  ascertained 
as  before.  For  each  addition  of  solute  there  is  a  cor- 
responding depression,  and  from  each  pair  of  values 
the  molecular  weight  of  the  dissolved  substance  may  be 

calculated   by  the   formula   M=-^~f   already   discussed. 

v 

The  value  obtained  for  M  by  this  method  ought  not 
to  differ  from  the  correct  value  by  more  than  3—5  per 
cent. 

In  the  most  accurate  work  it  is  necessary  to  adjust 
the  temperature  of  the  external  bath  so  that  it  is  only 
slightly  below  the  freezing  point  of  the  solution  in  A. 
This  is  conveniently  done  for  aqueous  solutions  by  putting 


110  PHYSICAL  CHEMISTRY 

ether  in  the  external  bath  and  aspirating  a  current 
of  air  through  it.1  By  regulating  the  current  of  air,  any 
desired  temperature  between  0D  and  —15°  is  easily  main- 
tained. 

Biological  Applications. — The  difficulties  involved  in 
the  direct  determination  of  osmotic  pressure  have  been 
repeatedly  emphasised.  In  the  depression  of  the  freez- 
ing point,  however,  we  have  a  measure  of  the  osmotic 
pressure  of  a  solution  which  is  more  accessible  by  ordinary 
experimental  work,  and  the  freezing  point  method  has 
therefore  been  extensively  applied  in  studying  the  osmotic 
power  of  various  fluids  occurring  in  the  living  organism 
It  should  however  be  pointed  out  that  the  indirect  deter- 
mination of  osmotic  pressure  by  means  of  the  freezing 
point  is,  in  one  sense,  much  less  accurate  than  the  process 
of  direct  measurement.  For,  as  has  already  been  shown, 
the  osmotic  pressure  P  of  an  aqueous  solution  is  related 
to  the  freezing  point  depression  T0  -  T  by  the  formula 
P=  12'03(ro  -T)  atmos.,  and  it  appears  from  this  that 
to  a  freezing  point  depression  of  O001C,  which  it  is  very 
difficult  to  measure  with  any  approach  to  accuracy,  there 
corresponds  an  osmotic  pressure  of  9  mm.  of  mercury, 
a  quantity  which  can  be  accurately  determined.  In  the 
absence,  however,  of  trustworthy  and  rapidly  acting 
semi- permeable  membranes  the  more  practical  if  less 
accurate  freezing  point  method  of  studying  osmotic 
pressure  is  used  by  the  ordinary  worker. 

In  the  ordinary  form  of  the  Beckmann  freezing  point 
apparatus  10-20  cub.  cm.  of  liquid  are  required  for  a 
determination.  It  is  sometimes  difficult,  however,  if  not 
impossible,  to  obtain  this  quantity  of  a  fluid  from  an 
organism,  and  hence  if  the  osmotic  value  for  such  a 
fluid  is  to  be  determined  by  the  freezing  point  method, 

1  Raoult,  Zeit.  physical.  (7Aem.,-1898,  27,  617. 


FREEZING   POINT  111 

an  apparatus  permitting  the  use  of  a  smaller  quantity 
of  liquid  is  desirable.  With  this  end  in  view,  modified 
forms  of  apparatus  have  been  introduced,  such  as  that 
described  by  Guye  and  Bogdan,1  which  differs  from 
the  Beckmann  apparatus  chiefly  in  having  a  smaller 
freezing  tube  and  a  smaller  thermometer  bulb.  An 
experiment  can  be  carried  out  with  1*5  cub.  cm.  of  liquid, 
and  the  authors  claim  that  the  results  are  nearly  as 
accurate  as  those  obtained  with  the  usual  apparatus  under 
ordinary  working  conditions. 

The  freezing  point  method  has  been  extensively  used 
in  studying  the  osmotic  pressure  of  the  blood  from 
different  animals,  and  the  variations  in  this  pressure 
resulting  from  changes  in  the  external  conditions.  It 
is  immaterial  whether  defibrinated  blood  or  blood  serum 
is  taken  for  the  determination  of  the  freezing  point, 
since  the  corpuscles,  like  other  suspended  particles,  have 
110  influence  on  the  osmostic  pressure.  Further,  blood 
plasma  and  blood  serum  have  practically  the  same 
freezing  point,  a  little  proteid  more  or  less  making  nc 
appreciable  difference. 

Numerous  investigations  have  shown  that  the  freezing 
point  of  mammalian  blood  does  not  vary  much  from 
one  species  to  another.  This  is  brought  out  by  the 
following  figures: — 

Animal.  Freezing  Point  of  Blood. 

Man -0-56 

Ox -0-58 

Horse -0'56 

Rabbit -0'59 

Cat -0-63 

Dog -0-57 

Sheep -0-62 

Nor  is  there  much  variation  from  time  to  time  in  the 

1  Journ.  chim.  phys.,  1903,  1,  379.     * 


112  PHYSICAL  CHEMISTRY 

osmotic  pressure  of  the  blood  of  one  individual,  a  fact 
that  may  be  contrasted  with  the  behaviour  of  urine  in 
this  respect.  Even  in  the  case  of  a  healthy  person,  the 
freezing  point  of  the  urine  varies  within  very  wide  limits 
in  the  course  of  twenty-four  hours,  and,  according  to 
Bouchard.1  while  the  normal  freezing  point  of  undiluted 
urine  may  be  taken  as  about  — 1'35°,  it  may  vary  from 
—  0'50°  to  —  2'24°  in  different  pathological  conditions. 

Another  direction  in  which  the  freezing  point  method 
has  been  applied  is  in  the  study  of  the  relation  between 
the  osmotic  pressure  of  the  blood  of  fishes  and  that  of 
the  surrounding  medium.  In  the  case  of  all  invertebrate 
marine  animals  the  freezing  point  of  the  blood-  or  body 
fluid  is  the  same  as  that  of  the  water  in  which  they 
live.  Further,  these  organisms  are  unable  to  preserve 
any  difference  between  the  osmotic  pressure  of  their 
body  fluid  and  that  of  the  surrounding  medium ;  when 
the  osmotic  pressure  of  the  latter  is  artificially  varied  by 
dilution  or  concentration  the  body  fluid  undergoes  a  cor- 
responding change,  as  shown  by  the  freezing  point.  This 
is  illustrated  by  the  figures  in  the  following  table,  bearing 
on  the  behaviour  of  a  species  of  crab  (Maia  verrucosa). 
The  figures  under  I.  are  the  freezing  points  of  sea- 
water  (normal  and  artificially  modified),  while  the  figures 
under  II.  are  the  freezing  points  of  the  body  fluid  of 
the  crab  after  immersion  for  some  time  in  the  corre- 
sponding water : — 

i.  i. 

Normal  sea-water -2*3°  -  2'3° 

Concentrated  sea-water         ...     -  2'98°  -  2'9° 

Diluted  sea-water -1-38°  -  T4° 

It  is  obvious  that  the  organism  is  unable  to  regulate 
the  osmotic  pressure  of  its  body  fluid. 

In   the   case,    however,    of    many   marine   vertebrates 
1  Compt.  rend,  1899,  128,  6£. 


FEEEZING   POINT  113 

the  osmotic  pressure  of  the  blood  or  body  fluid  is  quite 
different  from  that  of  the  surrounding  medium,  and 
variation  in  the  osmotic  pressure  of  the  latter  is  accom- 
panied by  only  a  slight  variation  of  the  former.  This 
point  is  well  illustrated  by  some  observations  of  Dakin 1 
on  the  blood  of  fish  taken  from  sea-water  of  naturally 
varying  concentration.  He  determined  the  freezing  point 
of  the  blood  of  plaice  caught  in  Kiel  harbour,  in  the 
open  Baltic,  in  the  Kattegat,  and  off  Helgoland.  The 
freezing  points  of  the  water  in  the  four  cases  were 
respectively  -1-09°,  -1-30°,  -1-66°,  and  -1-90°,  while 
the  freezing  points  of  the  blood  of  the  plaice  were 
-0-66°,  -0-72°,  -0-73°,  -0'79°.  The  osmotic  pressure, 
therefore,  of  the  blood  of  the  plaice  is  dependent  only 
to  a  very  limited  extent  on  the  osmotic  pressure  of 
the  surrounding  medium.  The  codfish  is  still  more  in- 
dependent, and  any  variation  observed  in  the  freezing 
point  of  the  blood  in  this  case  is  covered  by  individual 
differences.  With  elasmobranchs,  on  the  other  hand, 
the  osmotic  pressure  of  the  blood  is  almost  the  same 
as  that  of  the  surrounding  sea-water,  and  as  this 
increases  in  density,  so  the  osmotic  pressure  of  the 
blood  changes.  It  is  found  in  general  that  the  freezing 
point  of  the  blood  of  marine  teleosts  taken  from  the 
North  Sea  is  on  the  average  about  —075°,  whilst  that 
of  the  blood  of  fresh-water  teleosts  averages  about 
—  0'53° ;  in  each  case  the  organism  is  largely  inde- 
pendent, so  far  as  osmotic  pressure  is  concerned,  of 
the  medium  in  which  it  lives. 

1  Biochem.  Journ.,  1908,  3,  258,  473. 


CHAPTER  VII 

THE   BEHAVIOUR    OF   SALTS,    ACIDS,    AND   BASES 
IN    AQUEOUS   SOLUTION 

Facts  apparently  Inconsistent  with  Avogadro's  Hypo- 
thesis.— The  acceptance  of  Avogadro's  hypothesis  was 
retarded  by  the  discovery  of  certain  cases  in  which  the 
molecular  weight  of  a  substance,  deduced  from  its  vapour 
density,  was  quite  out  of  harmony  with  the  formula  which 
seemed  probable  on  grounds  of  chemical  analogy.  The 
vapour  density  of  ammonium  chloride,  for  instance,  is  only 
about  half  what  it  ought  to  be  if  NH4C1  is  the  correct 
formula  for  this  compound ;  on  the  other  hand,  the  vapour 
density  of  acetic  acid  has  a  value  greater  than  corre- 
sponds to  the  formula  CH3.COOH.  In  the  extension 
of  Avogadro's  hypothesis  to  solutions  similar  difficulties 
have  been  encountered.  Cases  are  known  in  which  the 
molecular  weight  of  a  dissolved  substance,  calculated 
from  the  depression  of  the  freezing  point  or  one  of 
the  other  osmotic  properties,  is  greater  than  the  value 
which  corresponds  with  the  ordinarily  accepted  formula. 
Just  as  the  vapour  density  of  acetic  acid  is  abnormally 
high,  so  the  molecular  weight  of  acetic  acid  dissolved 
in  benzene,  deduced  from  its  influence  on  the  freezing 
point  of  benzene,  is  nearly  double  the  value  which 
corresponds  to  the  formula  CH3.COOH.  High  values 
are  similarly  obtained  for  the  molecular  weight  in 
benzene  solution  of  all  substances  containing  the  —OH 
group,  phenol  and  alcohol,  for  instance.  A  glance  at 


SALT   SOLUTIONS  115 

the   formula   by   which   molecular   weight   is   calculated 

k  o 
from,  the  depression  of  the  freezing  point,  M  =  —  '-^-  (see 

p.  107),  shows  that  an  abnormally  large  value  for  the  mole- 
cular weight  is  the  result  of  an  abnormally  small  depres- 
sion. Now  the  depression  of  the  freezing  point,  like  the 
osmotic  pressure,  is  a  measure  of  the  number  of  dissolved 
units,  and  hence  an  abnormally  small  depression  points  to 
a  reduction  in  the  number  of  dissolved  units  below  the 
figure  which  we  should  expect  from  the  amount  of 
substance  actually  in  solution.  Such  a  reduction  must 
be  due  to  the  clubbing  together,  or  association,  of  the 
normal  molecules  to  form  larger  aggregates. 

Abnormally  Great  Depressions  of  the  Freezing 
Point.  —  More  interesting  perhaps  are  the  cases,  the 
deviation  of  which  from  the  normal  is  in  the  opposite 
direction.  There  are  very  many  substances  the  mole- 
cular weights  of  which,  calculated  from  their  influence 
on  the  freezing  point  of  water,  are  quite  inconsistent 
with  the  accepted  formulae.  A  solution  of  sodium  chloride, 
for  instance,  containing  1'135  gram  of  the  salt  in  100 
grams  of  water,  freezes  at  -0'687°.  Taking  &=18'60 
for  water  (see  p.  107),  and  calculating  the  molecular  weight 
of  the  dissolved  substance  in  the  usual  way,  we  obtain 

5  =  30'7,  a  value  far  below  58-5,  which  is 


the  molecular  weight  for  sodium  chloride,  on  the  assump- 
tion that  it  contains  one  atom  of  sodium  and  one  of 
chlorine.  In  the  case  of  other  salts  also,  as  well  as 
for  many  acids  and  bases,  there  is  an  equally  marked 
discrepancy  between  the  accepted  formula  of  the  sub- 
stance and  the  molecular  weight  deduced  from  its  osmotic 
behaviour.  A  more  definite  conception  of  the  extent 
of  the  discrepancy  will  be  gained  by  a  glance  at  the 
figures  in  the  following  tables.  In  the  first  column  of 


116  PHYSICAL   CHEMISTRY 

each  table  is  recorded  the  strength  of  the  solution  in 
gram-molecules  per  litre;  the  second  column  contains 
the  observed  depressions  t,  and  the  third  column  contains 

the  values  i  =  7 - ,  tQ  being  the  depression  which  would 
be  observed  if  the  solute  behaved  normally : — 

Sodium  Chloride.  Sodium  Sulphate. 

Concentration.         t.  t=   .  Concentration.         t.  i=-. 

0-117  0-424°  1-93  0'028  0-141°  2*66 

0-194  0-687°  1-87  0'070  0'326°  2'46 

0-324  1-135°  1-86  0-117  0'515°  2-33 

0-539  1-894°  1-85  0'195  0'817°  2-21 

These  figures,  and  many  others  which  might  be  quoted, 
show  that  the  depression  of  the  freezing  point  of  water 
caused  by  salts  is  abnormally  great,  a  fact  that  points 
to  an  increase  in  the  number  of  dissolved  units  above 
the  figure  which  we  should  expect  from  the  amount 
of  salt  actually  present  in  any  solution.  From  the 
figures  obtained  by  Arrhenius,1  it  appears  that  for  salts 
of  the  type  of  sodium  chloride  the  values  of  i  run  up 
to  2,  while  for  salts,  such  as  sodium  and  potassium 
sulphates,  magnesium,  calcium  and  strontium  chlorides, 
the  values  run  up  to  3.  Evidence  of  this  enhanced 
osmotic  activity  on  the  part  of  salts  is  found  also  in 
the  values  of  the  isotonic  coefficients  tabulated  on  p.  72. 
The  isotonic  coefficients,  it  must  be  remembered,  repre- 
sent the  relative  osmotic  pressures  of  equimolecular 
solutions,  and  the  figures  for  the  isotonic  coefficients 
show  that  sodium  chloride  and  potassium  nitrate  exhibit 
an  osmotic  activity  which  is  about  1-7  times  as  great r 
while  calcium  chloride  exhibits  an  osmotic  activity  which 
is  2-3  —  2-4  times  as  great  as  that  of  sucrose  taken  as- 
the  normal  substance. 

As  already  indicated,   this  enhanced  osmotic  activity 

1  Zeit.  physikal.  Chem.,  1888,  2,  491. 


SALT  SOLUTIONS  117 

on  the  part  of  salts  points  to  an  abnormally  large  number 
of  dissolved  units  in  their  solutions.  How  is  this  to  be 
explained?  Reference  has  been  made  to  the  fact  that 
ammonium  chlorj.de  and  other  substances  are  found  to 
have  vapour  densities  much  below  the  values  correspond- 
ing to  their  accepted  f@rmula3.  This  exceptional  be- 
haviour has  been  reconciled  with  Avogadro's  hypothesis 
by  assuming  a  dissociation  of  the  vaporised  molecule 
into  two  or  more  simpler  molecules ;  in  the  case  of 
ammonium  chloride,  indeed,  direct  evidence  is  obtain- 
able, showing  that  when  the  substance  is  vaporised  it 
breaks  up  into  ammonia  and  hydrogen  chloride,  giving 
two  molecules  in  place  of  one.  Between  the  case  of 
these  abnormally  low  vapour  densities  and  the  case  of 
abnormally  great  depressions  of  the  freezing  point  of 
water  there  is  a  historical  parallel  in  that  a  dissociation 
hypothesis  has  been  brought  forward  also  to  account 
for  the  exceptional  osmotic  behaviour  of  salts  (acids 
and  bases)  in  aqueous  solution. 

The  Electrolytic  Dissociation  Hypothesis. — In  1887 
Arrhenius  propounded  the  view1  that  acids,  bases,  and 
salts  in  aqueous  solution  are  dissociated  to  a  greater  or 
less  extent  into  positively  and  negatively  charged  particles 
or  'ions,'  and  that  the  increase  in  the  number  of  units 
in  solution  which  arises  from  this  dissociation  is  re- 
sponsible for  the  abnormally  high  osmotic  activity  of 
these  substances.  Sodium  chloride,  according  to  this 
hypothesis,  splits  up  to  a  large  extent,  when  dissolved 

in  water,  into  positively  charged  sodium  ions  Na,  and 
negatively  charged  chlorine  ions  Cl ;  potassium  nitrate 

i  

similarly  dissociates  into  K  and  N03.  3     In  both  these 

1  Zeit.  physikal.  Chem  ,  1887,  1,  631. 

2  Positive  ions  are  very  frequently  indicated  by  dots,  negative  ions 
by  dashes  ;  thus— Na',  H',  NH4\  01',  NO/. 


118  PHYSICAL  CHEMISTRY 

+    — 

cases,  as  also  in  others,  such  as  hydrochloric  acid  (H,  Cl), 

+ 
potassium     hydroxide     (K,     OH),     potassium     acetate 

+  + 

(K,  CH3.COO),  and  ammonium  chloride  (NH4,  Cl),  one 

molecule  produces  two  ions,  so  that  even  on  the  sup- 
position of  complete  dissociation  the  abnormal  osmotic 
effect  of  these  compounds,  whether  measured  by  the 
lowering  of  vapour  pressure,  jbhe  elevation  of  the  boil- 
ing point,  or  the  depression  of  the  freezing  point  of 
water,  cannot  be  greater  than  twice  the  effect  pro- 
duced by  an  equimolecular  quantity  of  a  normal  sub- 
stance. In  harmony  with  this  it  is  found,  as  already 
stated,  that  the  values  of  i  for  sodium  chloride,  potassium 
nitrate,  and  the  like,  run  up  to  2.  According  to  Arrhenius, 

sodium  sulphate  in  aqueous  solution  is  more  or  less  dis- 

+       + 
sociated   into   three   ions,    Na,    Na,    and    S04,   the   last 

carrying  a  double  negative  charge ;  similarly,  calcium 
chloride  produces  three  ions,  one  with  a  double  positive 

+  + 
charge  Ca,  and  two  with  a  single  negative  charge  Cl,  Cl. 

In  both  these  cases,  and  in  analogous  compounds,  one 
molecule  produces  three  ions,  and  on  the  supposition 
of  complete  dissociation  the  abnormal  osmotic  effect 
would  be  three  times  the  effect  due  to  an  equimolecular 
quantity  of  a  normal  substance.  In  harmony  with  this 
it  is  found  that  the  values  of  i  for  sodium  and  potassium 
sulphates,  magnesium,  calcium,  and  strontium  chlorides, 
and  other  analogous  compounds,  run  up  to  3. 

If  this  hypothesis  of  the  ionic  dissociation  of  salts,  acids, 
and  bases  in  aqueous  solution  is  accepted,  then  we  can 
deduce  the  degree  or  extent  of  the  dissociation  in  any 
solution  by  comparing  the  observed  depression  t  of  the 
freezing  point  with  the  depression  t0  which  would  be 
observed  were  there  no  dissociation;  the  latter  value  is 

calculated  by  the  formula  £0  =  —i^,  in  which  M  is  the 


I 

SALT  SOLUTIONS  119 

normal  molecular  weight  of  the  dissolved  substance. 
Suppose  that  of  100  molecules  of  a  dissolved  salt  the 
fraction  a  has  undergone  dissociation,  each  dissociated 
molecule  producing  n  ions,  then  there  remain  in  the 
undissociated  condition  100(1  — a)  molecules.  The 
number  of  molecules  which  have  undergone  disso- 
ciation is  lOOa,  and  the  number  of  ions  so  produced  is 
lOOaX^;  the  total  number  of  units  in  solution  is 
therefore  100(1  —  a)  +  WOan,  and  the  actually  observed 
depression  t  of  the  freezing  point  must  be  proportional 
to  this  figure.  If,  on  the  other  hand,  there  were  no 
dissociation  the  number  of  units  in  solution  would  be 
merely  100,  and  to  this  figure  there  would  correspond 
the  depression  tQ.  Since  the  depressions  are  propor- 
tional to  the  numbers  of  units  present  in  solution, 

t      100(l-a)  +  100a?i  .  t-t^ 

--  -^  1 +(,-!>,  so  that  a  =  (-^; 

or  if  —  be  expressed  by  the  symbol  i,  a  =  ^—.     If    this 
t0  n-l 

formula  is  applied  to  the  data  bearing  on  the  freezing 
points  of  sodium  chloride  and  sodium  sulphate  solutions 
(see  p.  116),  it  appears  that  in  a  sodium  chloride  solution 
containing  0'2  of  a  gram-mol.  per  litre,  85-90  per  cent, 
of  the  salt  is  dissociated  into  its  ions,  and  in  a  sodium 
sulphate  solution  of  the  same  strength  about  60  per  cent, 
of  the  salt  is  so  dissociated.  It  appears  also  from  the 
figures  on  p.  116  that  the  more  dilute  the  solution 
the  greater  is  the  percentage  of  salt  in  the  dissociated 
condition, 

Ionic  Dissociation  and  Electrolytic  Conduction. — The 

claim  which  the  hypothesis  of  ionic  dissociation  makes 
on  our  consideration  is  greatly  strengthened  by  the  fact 
that  it  not  only  furnishes  an  explanation  of  the  abnormal 
osmotic  influence  of  acids,  bases,  and  salts  in  aqueous 
solution,  but  gives  also  an  intelligible  interpretation  of 


120  PHYSICAL   CHEMISTRY 

various  other  phenomena.  It  is  well  known  that  a 
solution  of  sugar  or  alcohol  in  water  is  no  better  a  con- 
ductor of  the  electric  current  than  water  itself;  sugar 
and  alcohol  are  non-electrolytes.  On  the  other  hand, 
there  are  many  substances  the  aqueous  solutions  of  which 
are  relatively  good  conductors  of  the  electric  current.  As 
Arrhenius  pointed  out,  these  are  precisely  the  substances 
which  have  an  abnormally  great  effect  in  raising  the 
boiling  point  or  lowering  the  freezing  point  of  water. 
Sugar  and  alcohol  are  non-electrolytes ;  their  effect  on 
the  freezing  point  of  water  is  normal.  Sodium  chloride, 
potassium  nitrate,  hydrochloric  and  sulphuric  acids  are 
electrolytes ;  their  aqueous  solutions  conduct  the  electric 
current,  and  they  undergo  decomposition  under  the  in- 
fluence of  the  current;  they  are  also  among  the  sub- 
stances which  produce  an  abnormal  depression  of  the 
freezing  point. 

All  this  becomes  intelligible  if  it  is  supposed  that  this 
latter  class  of  substances  is  liable  to  ionic  dissociation. 
For,  according  to  Arrhenius's  hypothesis,  a  solution  of 
sodium  chloride,  to  take  one  of  the  substances  which 
have  an  abnormal  influence  on  the  freezing  point  of 
water,  contains  a  large  proportion  of  dissociated  mole- 
cules in  the  form  of  positively  and  negatively  charged 
ions.  Accordingly  when  two  electrodes,  one  charged 
positively  and  the  other  negatively,  are  immersed  in 
such  a  solution,  an  attractive  force  is  exerted  on  the 
ions  of  opposite  sign.  Under  the  influence  of  this 
force  the  positively  charged  ions  move  towards  the 
negative  electrode,  and  the  negatively  charged  ions 
towards  the  positive  electrode.  The  passage  of  an 
electric  current,  then,  through  a  solution  of  sodium 
chloride  or  any  other  electrolyte  consists  in  a  stream- 
ing of  positive  ions  in  one  direction  and  of  negative 
ions  in  the  opposite  direction.  The  neutral  or  undis- 


SALT  SOLUTIONS  121 

sociated  molecules  are  unaffected;  they  are  not  charged, 
and  experience  no  impulse  to  move  rather  in  one  direc- 
tion than  another ;  they  are  inactive  so  far  as  the 
transport  of  electricity  through  the  solution  is  con- 
cerned. 

On  the  basis  of  this  view,  the  efficiency  of  a  given 
quantity  of  a  salt  in  conducting  the  current  must 
depend  on  the  extent  to  which  the  salt  is  dissociated ; 
if  the  degree  of  dissociation  is  high,  then  the  propor- 
tion of  current-carriers  will  be  high  also,  and  the  power 
of  conducting  the  current,  the  conductivity  as  it  is 
called,  will  be  relatively  great.  A  solution  of  a  sub- 
stance, on  the  other  hand,  which  is  ionised  only  to  a 
small  extent,  will  be  a  relatively  poor  conductor  of  the 
electric  current.  It  is  further  obvious  that  if  we  could 
compare  the  conductivity  of  an  actual  sodium  chloride 
solution  with  the  conductivity  which  the  same  amount 
of  the  salt  would  exhibit  if  it  were  completely  ionised, 
we  should  obtain  a  measure  of  the  dissociation  in  the 
actual  solution. 

Increase  of  ConductiYity  with  Dilution.— The  figures 
recorded  on  p.  116  for  solutions  of  sodium  chloride  and 
sodium  sulphate  show  that  the  degree  of  dissociation  in- 
creases as  the  solutions  become  less  concentrated,  i.e.  as  the 
dilution  increases,  and  this  is  a  statement  that  applies  to 
dilute  aqueous  solutions  of  all  electrolytes,  so  far  as  the 
freezing  point  evidence  goes.  It  is  therefore  to  be  expected, 
on  the  basis  of  the  ionic  dissociation  hypothesis,  that  for  a 
.given  quantity  of  a  salt  the  conducting  efficiency — the  con- 
ductivity— should  become  greater  as  the  concentration  of 
the  solution  decreases.  This  is  what  actually  takes  place,  as 
•can  be  demonstrated  by  the  following  simple  experiment : — 

A  rectangular  glass  jar  is  procured,  say  about  25  cm. 
Mgh,  4  cm.  wide,  and  10  cm.  long,  and  two  strips  of  sheet 


122  PHYSICAL   CHEMISTRY 

copper  are  cut  to  fit  the  opposite  ends  of  the  jar  from 
top  to  bottom ;  the  top  ends  of  the  strips  should  project 
somewhat  beyond  the  mouth  of  the  jar,  and  are  provided 
with  binding  screws.  The  two  strips  are  kept  pressed  up 
against  the  opposite  ends  of  the  jar  by  glass  rods,  the 
ends  of  which  are  inserted  into  rubber  stoppers,  the  total 
length  of  the  rods  +  the  stoppers  being  adjusted  to  the 
distance  between  the  strips.  A  little  concentrated  sodium 
acetate  solution  is  introduced  into  the  jar,  and  the  latter 
put  in  series  with  a  sulphuric  acid  voltameter,  fitted  with 
a  delivery  tube  so  that  the  gas  liberated  when  a  current 
is  passing  may  be  collected  in  an  inverted  tube  filled 
with  water.  In  this  arrangement  the  rate  at  which  the 
bubbles  of  gas  pass  up  the  tube  is  roughly  a  measure 
of  the  strength  of  the  current  passing  through  the  volta- 
meter and  any  other  piece  of  apparatus  which  is  in 
series  with  it.  A  current  is  now  sent  through  the  jar  and 
the  voltameter,  and  is  so  regulated  that  a  bubble  of  gas 
ascends  in  the  water  tube  once  in  two  seconds  or  there- 
abouts. As  soon  as  the  current  is  adjusted,  distilled 
water  is  poured  continuously  into  the  jar  until  it  is  full. 
In  this  way  the  sodium  acetate  solution  is  diluted  without 
altering  the  quantity  of  salt  which  is  between  the  elec- 
trodes, and  which  is  therefore  available  for  conduction 
of  the  current.  This  progressive  dilution  of  the  salt 
solution  is  accompanied  by  a  gradual  increase  in  the  rate 
of  evolution  of  gas  from  the  voltameter,  which  points 
to  an  increase  in  the  strength  of  the  cur::ent  which  is 
passing.  The  resistance,  therefore,  which  the  current 
experiences  between  the  electrodes  in  the  jar  is  diminished 
by  dilution  of  the  sodium  acetate  solution ;  that  is,  the 
conducting  efficiency  of  the  salt  which  is  between  the 
electrodes,  and  which  is  constant  in  quantity  throughout 
the  experiment,  increases  with  dilution.  If  a  concentrated 
acetic  acid  solution  is  put  in  the  jar  instead  of  sodium 


SALT  SOLUTIONS 


123 


acetate  solution,  and  the  current  is  suitably  adjusted,  a 
similar  result  is  obtained,  except  that  the  increase  in 
the  rate  of  evolution  of  the  bubbles  with  dilution  is  much 
more  marked  in  this  case.  The  increase  of  conductivity 
with  dilution  is  therefore  more  rapid  for  acetic  acid  than 
for  sodium  acetate. 

Measurement  of  Conductivity. — The  experiment  just 
described  demonstrates  qualitatively  the  increase  of  con- 
ductivity with  dilution,  but  it  is  easy  to  get  a  quantitative 


measure  of  this  change  by  determining  the  conductivity. 
The  determination  of  the  conductivity  of  a  solution 
resolves  itself  into  the  determination  of  the  resistance, 
and  this  is  effected  by  a  modification  of  the  ordinary 
Wheatstone  bridge  method.  The  arrangement  of  the 
apparatus  necessary  for  the  determination  of  the  resist- 
ance of  a  solution  is  represented  diagrammatically  in 
Fig.  15,  where  B  is  a  resistance  box,  C  is  a  cell  containing 
the  solution  ;  cib  is  the  bridge  wire.  The  ends  a  and  b 
of  the  bridge  wire  are  connected  with  the  small  induction 
coil  I,  which  gives  an  alternating  current.  This  is  neces- 


124 


PHYSICAL  CHEMISTEY 


sary  in  order  to  avoid  the  polarisation  effects  which  would 
make  themselves  felt  if  a  continuous  current,  such  as  is 
usually  employed  in  the  Wheatstone  bridge  method,  were 
passed  through  the  solution  in  C.     The  use  of  an  alter- 
nating current  necessitates  the  replacement  of  the  ordinary 
galvanometer  by  an  instrument  which  will  respond  to 
such  a  current.     A  telephone  is  usually  employed,  and, 
as  shown  at  T  in  the  diagram,  it  is  connected  on  the 
one  hand  with  the  point  d,  and  on  the  other  with  the 
moving  contact  c.     When  the  apparatus  is  ready,  the  in- 
duction coil  is  operated  by  the  accumulator  A,  and  the 
^  moving  contact  is  so  adjusted  on  the 
~^~&-\        /^TJ         wire  db  that  there  is  no  sound  in  the 
m       m  telephone.     It  follows  then,  according 

to  well-known  principles,  that 

••••••I  Resistance  in  C  _  Length  he  f 

Resistance  in  B      Length  ac  ' 

as  the  resistance  in  B  is  known  and  the 
lengths  ac  and  be  are  easily  ascertained 
on  the  scale  over  which  the  bridge  wire 
is  stretched,  the  resistance  of  the  cell 
can  be  calculated. 

Various  types  of  cell  are  employed 
according  as  the  resistance  of  the 
solution  is  high  or  low.  One  of  the 
most  generally  serviceable  is  shown  in 
Fig.  16.  The  electrodes  E  are  made  of 
stout  platinum  foil,  and  are  in  electrical 
connection  with  the  mercury  in  the  glass 
tubes  TT  by  means  of  two  pieces  of  stout  platinum  wire 
sealed  through  the  ends  of  these  tubes.  Connection  is 
made  with  the  rest  of  the  apparatus  by  copper  wires 
which  dip  in  the  mercury.  The  tubes  TT  are  fitted 
tightly  in  the  ebonite  lid  of  the  cell,  so  that  the  electrodes 
may  be  lifted  out,  rinsed  and  driecT  without  their  relative 


FIG.  16. 


SALT   SOLUTIONS  125 

position  being  altered  in  the  slightest.  Before  the  cell 
is  used  the  electrodes  are  platinised,  that  is,  coated  with 
a  fine  deposit  of  platinum  black.  This  is  done  by  electro- 
lysing a  solution  of  platinic  chloride  in  the  cell,  the 
electrodes  being  made  alternately  cathode  and  anode. 

It  is  customary  to  compare  the  resistance  and  con- 
ductivity of  solutions  with  the  resistance  and  conductivity 
of  a  hypothetical  liquid  which,  if  enclosed  in  a  centi- 
metre cube,  would  offer  a  resistance  of  1  ohm  between 
two  opposite  faces  of  the  cube  acting  as  electrodes.  In 
dealing  with  the  density  of  liquids  and  solids  we  take 
water  as  the  standard,  and  speak  then  of  the  specific 
gravity  of  a  substance;  similarly,  in  dealing  with  the 
resistance  and  conductivity  of  solutions  we  take  the 
said  hypothetical  liquid  as  the  standard,  and  speak  then 
of  the  specific  resistance  arid  the  specific  conductivity 
of  a  solution.  The  specific  resistance  of  a  solution  there- 
fore is  simply  the  number  which  represents  the  resistance 
in  ohms  of  a  column  of  the  solution  1  sq.  cm.  in  section 
and  1  cm.  long.  The  actual  conducting  column  in  the 
cell  C  has  the  resistance  r,  and  if  we  suppose  that  the 
distance  between  the  electrodes  is  /  cm.,  and  that  the 
section  of  the  conducting  column  is  s  sq.  cm.,  then  R, 
the  specific  resistance  of  the  solution,  is  obtained  by 

o 

the   formula    R  =  TJ.    The  conductivity  of  a  solution  is 

t 

the  reciprocal  of  the  resistance,  so  that  if  we  take  K  to  re- 
present specific  conductivity,  we  have  K  =  —  =  ~.  -.  The 

±1     r     s 

evaluation  of  the  specific  conductivity  depends  therefore 
on  the  dimensions  of  the  cell  used,  as  well  as  on  the 
observed  resistance  r.  For  most  ordinary  cells  it  would 
be  impossible  to  obtain  the  exact  values  of  I  and  s  by 
mere  measurements  of  length,  and  the  device  is  usually 
Adopted  of  first  charging  the  cell  with  a  solution  the 


126  PHYSICAL  CHEMISTRY 

specific  conductivity  KQ  of  which  has  been  accurately 
determined  by  special  experiments.  Such  a  solution  is 

-S-KC1,    for    which    KO  =  0*002768    at    25°,   or  ^-KCl, 

for  which  *0  =  0'001412  at  25°.  These  exact  values  have 
been  obtained  by  determining  the  resistance  of  the 
solutions  in  cells  for  which  /  and  s  could  be  accurately 
determined.  Suppose,  then,  that  in  an  actual  experiment 

N 

the     cell    is    charged    first    with    _KC1,  and  secondly 

o\J 

with  the  solution,  the  specific  conductivity  (K)  of  which 
is  to  be  found ;  further,  that  the  resistances  measured 
in  the  two  cases  are  respectively  TO  and  r  at  25  ~. 
Subject  to  the  condition  that  the  relative  position  of 
the  electrodes  has  remained  the  same  throughout  the 

experiment,  *n= and  K=-.  -,    whence    it     follows 

r0   s  r    s 

that  K  =  KO  .  -9.    The  value  of  KO  is  known,  the  values  of 
r 

rQ  and  r  have  been  determined,  so  that  K.  is  obtained  by 
a  simple  calculation. 

It  ought  to  be  pointed  out  here  that  all  solutions 
used  in  determinations  of  conductivity  are  prepared  with 
specially  pure  water.  Ordinary  distilled  water  is  re- 
distilled under  certain  conditions,  and  thus  freed  from 
various  impurities  which  add  to  its  conducting  power. 
The  question  as  to  how  far  this  purification  of  water 
can  be  carried  will  be  discussed  later  (p.  170). 

Specific  Conductivity  and  Equivalent  Conductivity. — 
When  solutions  of  a  salt  of  gradually  decreasing  con- 
centration are  examined,  it  is  found  that  the  specific 
conductivity  regularly  diminishes.  This  falling  off  in 
the  specific  conductivity  with  increasing  dilution  is  illus- 
trated by  the  figures  in  the  first  two  columns  of  the 
following  table,  which  refers  to  sodium  chloride.  The 


SALT   SOLUTIONS 


127 


figures  in  the  first  column  are  the  concentrations  of 
the  salt  in  gram- equivalents  per  litre  of  solution,  those 
in  the  second  column  are  the  corresponding  values  of 
the  specific  conductivity  at  25°;  the  significance  of  the 
figures  in  the  third  column  will  be  explained  presently. 


Concentration. 
0-0312 
0-0156 
0-0078 
0-0039 


K. 

0-00356 
0-00183 
0-000938 
0-000476 


X. 

114-1 
117-4 
120-1 
122*0 


That  the  specific  conductivity  should  diminish  with 
increasing  dilution  is  only  to  be  expected,  for  its  value 
is  in  each  case  based  on  the  resistance  between  two 
opposite  faces  of  a  centimetre  cube  filled  with  the 
solution.  Now  as  the  solution  is  gradually  diluted  there 
will  be  less  and  less  of  the  salt  in  this  centimetre  cube, 
less  and  less  therefore  of  the  substance  which  acts  as 
the  carrier  of  the  current,  for  the  water  is  a  non-con- 
ductor, or  at  all  events  an  exceedingly  poor  conductor. 
It  is  quite  natural,  then,  that  specific  conductivity, 
based  as  it  is  on  the  consideration  of  a  definite  volume 
of  the  solution,  should  diminish  with  dilution. 

If,  however,  we  are  to  ascertain  really  how  the 
efficiency  of  a  given  salt  in  conducting  the  current 
varies  with  dilution,  we  must  obtain  a  set  of  figures 
which  relate  to  the  same  quantity  of  the  salt  at  each 
dilution.  Such  figures  are  directly  deducible  from  the 
values  for  the  specific  conductivity.  Suppose  that  we  are 
dealing  with  a  normal  solution  of  sodium  chloride,  and 
that  we  have  an  electrolytic  cell  the  sides  of  which 
are  formed  by  electrodes  1000  sq.  cm.  in  area  and  exactly 
1  cm.  apart.  This  cell  would  hold  1  litre  of  the  normal 
solution,  and  the  quantity  of  salt  between  the  electrodes 
would  be  1  gram-equivalent.  Since  this  solution  may 
be  regarded  as  made  up  of  1000  centimetre  cubes,  the 

i 


128  PHYSICAL   CHEMISTRY 

figure  which  represents  the  conducting  power  of  the 
1  gram-equivalent  of  salt  will  be  1000  times  the  figure 
which  stands  for  the  conductivity  of  a  centimetre  cube 
of  the  solution,  that  is,  1000*;,  where  K.  is  the  specific 
conductivity  of  a  normal  sodium  chloride  solution.  If, 
instead  of  a  normal  solution  of  sodium  chloride,  we  are 
dealing  with  a  half-normal  solution,  the  volume  of  the 
latter  containing  1  gram-equivalent  of  salt  is  2000 
cub.  cm.,  and  to  bring  this  gram-equivalent  between 
two  electrodes  which  are  1  cm.  apart,  the  area  of  each 
electrode  would  have  to  be  2000  sq.  cm.  The  bulk  of 
solution  between  the  electrodes  in  such  an  imaginary 
cell  might  be  regarded  as  made  up  of  2000  centimetre 
cubes,  and  the  figure  which  represents  the  conducting 
power  of  the  1  gram-equivalent  of  salt  will  be  2000 
times  the  figure  which  stands  for  the  conductivity  of 
a  centimetre  cube  of  the  solution,  that  is,  2000/c,  where 
K.  is  the  specific  conductivity  of  a  half-normal  sodium 
chloride  solution.  This  argument  might  obviously  be 
extended  to  cover  any  solution  of  sodium  chloride  or 
any  other  electrolyte,  but  enough  has  been  said  to 
show  that  a  measure  of  the  conducting  power  of  1  gram- 
equivalent  of  electrolyte  at  various  dilutions  is  to  be 
found  in  the  product — specific  conductivity  x  volume  of 
solution  in  cub.  cm.  which  contains  1  gram-equivalent. 
For  this  volume  of  solution  the  symbol  </>  is  generally 
taken,  and  the  conducting  power  of  a  gram-equivalent, 
the  equivalent  conductivity  as  it  is  termed,  is  represented 
by  the  symbol  X,  so  that  X  =  K  .  <j>. 

With  increasing  dilution,  as  already  indicated,  the 
specific  conductivity  diminishes ;  the  equivalent  con- 
ductivity, on  the  other  hand,  increases  steadily.  This 
statement  is  borne  out  by  the  figures  in  the  third 
column  of  the  table  on  p.  127,  and  in  greater  detail  by 
the  numbers  contained  in  the  following  table : — 


SALT   SOLUTIONS  129 

EQUIVALENT   CONDUCTIVITY  AT   18°. 


Gram-equivalents 
per  litre. 

KCl. 

CHs-COONa. 

HCl. 

NaOH. 

CHs.COOH. 

1-0 

98-3 

41-2 

301 

160 

1-32 

0-5 

102-4 

49-4 

327 

172 

2-01 

O'l 

112-0 

61-1 

351 

183 

4-60 

0-05 

115-9 

.64-2 

360 

190 

6-48 

o-oi 

122-4 

70-2 

370 

200 

14-3 

0-005 

124-4 

72-4 

373 

203 

20-0 

0-002 

126-3 

74-3 

376 

206 

30-2 

0-001 

127-3 

75-2 

377 

208 

41 

0-0005 

128-1 

75-8 

... 

... 

57 

0-0002 

128-8 

76-4 

... 

... 

80 

o-oooi 

129-1 

76-8 

... 

.  .. 

107 

The  cases  quoted  in  the  foregoing  table  are  merely 
instances  of  the  behaviour  of  aqueous  solutions  of 
electrolytes  generally,  and  there  is  therefore  no  doubt 
that  the  efficiency  of  an  electrolyte  as  a  conductor  of 
the  electric  current  increases  with  dilution.  The  figures 
in  the  table  supply  the  quantitative  basis  for  the  con- 
clusion of  which  a  qualitative  demonstration  has  been 
described  on  p.  122.  A  study  of  the  tabulated  values 
for  potassium  chloride,  sodium  acetate,  hydrochloric 
acid,  and  sodium  hydroxide  shows  that  \  is  increasing 
only  very  slightly  in  the  most  dilute  solutions,  that,  in 
fact,  it  tends  towards  a  maximum  value  which  could 
be  found  by  extrapolating  to  zero  concentration.  This 
may  be  done  on  the  basis  of  an  empirical  rule  dis- 
covered by  Kohlrausch,  who  showed  that  for  most 
electrolytes  in  dilute  solution  there  is  a  linear  relation- 
ship between  the  equivalent  conductivity  and  the  cube 
root  of  the  concentration.  The  value  thus  obtained  by 
extrapolation  is  known  as  the  equivalent  conductivity 
at  infinite  dilution,  and  is  indicated  by  the  symbol  \(X>. 
Such  an  extrapolation  can  be  safely  made  only  in  those 
cases  in  which  X  changes  but  slightly  in  the  most 
dilute  solutions  examined ;  it  would,  for  instance,  not 


130  PHYSICAL    CHEMISTRY 

be  permissible  in  the  case  of  acetic  acid,  where  X,  is 
increasing  rapidly  even  at  the  greatest  dilutions.  Where 
extrapolation  is  out  of  the  question,  another  method  of 
finding  the  value  of  \M  must  be  adopted,  a  method  that 
will  be  referred  to  later  (p.  152).  It  should  be  noted 
that  in  this  matter  of  extrapolation  acetic  acid  is  in  quite 
a  different  category  from  sodium  acetate,  and  the  fact 
that  the  relative  increase  in  X  between  TON  and  O0001N 
solutions  is  so  much  greater  for  acetic  acid  than  for 
sodium  acetate,  is  in  harmony  with  the  experiment 
described  on  p.  122. 

What  significance  is  to  be  attached  to  the  values 
of  X^?  According  to  the  electrolytic  dissociation  hypo- 
thesis, a  dissolved  electrolyte  takes  part  in  the  con- 
duction of  a  current  only  in  so  far  as  it  is  ionised, 
and  its  efficiency  in  conducting  the  current  will  from 
this  point  of  view  be  a  maximum  when  ionisatioii  is 
complete.  The  conducting  efficiency,  however,  is,  as 
we  have  seen,  at  a  maximum  in  infinitely  dilute  solution, 
and  therefore  the  value  of  X^  for  any  electrolyte  is 
to  be  taken  as  a  measure  of  the  total  number  of  ions 
that  can  be  produced  by  the  dissociation  of  1  gram- 
equivalent.  Similarly,  the  value  of  X  at  any  finite 
dilution  is  a  measure  of  the  number  of  ions  produced 
by  the  partial  dissociation  of  1  gram-equivalent  of  the 
electrolyte  under  these  conditions.  The  extent  to  which 
the  electrolyte  is  ionised,  the  degree  of  dissociation  (a), 

is  given  therefore  by  the  simple  formula  a  —  — . 

^30 

The  values  of  X^  at  18°  for  potassium  chloride,  sodium 
acetate,  hydrochloric  acid,  sodium  hydroxide,  and  acetic 
acid  are  129-9,  77-2,  383'3,  217-5,  and  351-7  respectively. 
On  the  basis  of  these  numbers  arid  of  the  figures  quoted 
in  the  table  on  p.  129,  the  following  values  of  a  have  been 
calculated  for  a  few  selected  concentrations :— 


SALT   SOLUTIONS  131 


ts     KCl. 

CHg.COONa 

.       HCl. 

NaOH. 

CHs.COOH. 

1-0 

0-76 

0-53 

0-79 

0-73 

0-004 

0-5 

0-79 

0-64 

0-85 

0-79 

0-006 

0-1 

0-86 

0-79 

0-91 

0-84 

0-013 

o-oi 

0-94 

0-91 

0-96 

0-92 

0-041 

O'OOl 

0-98 

0-97 

0-98 

0-96 

0-117 

This  table  shows  very  plainly  that  on  the  basis  of 
the  electrolytic  dissociation  hypothesis  we  must  regard 
potassium  chloride,  sodium  acetate,  hydrochloric  acid, 
and  sodium  hydroxide  as  being  highly  ionised  in  dilute 
solution,  and  a  similar  result  would  be  reached  by  a 
consideration  of  the  experimental  data  for  all  sodium 
and  potassium  salts  of  monobasic  acids,  for  nitric  acid 
and  potassium  hydroxide.  Acetic  acid,  on  the  other 
hand,  is  only  slightly  ionised  even  in  very  dilute  solution, 
and  in  this  respect  is  typical  of  many  monobasic  organic 
acids,  as  well  as  of  ammonia.  There  are  however  many 
acids  which,  as  regards  degree  of  dissociation,  are  in- 
termediate between  hydrochloric  acid  and  acetic  acid, 
just  as  there  are  many  bases  similarly  intermediate 
between  sodium  hydroxide  and  ammonia. 

Values  of  a  Obtained  by  Different  Methods.  —  Eefer- 
ence  has  already  been  made  to  the  fact  that  the  electrolytic 
dissociation  hypothesis  offers  an  explanation  not  only  of 
the  abnormal  osmotic  behaviour  of  acids,  bases,  and  salts 
in  aqueous  solution,  but  also  of  the  part  which  these 
compounds  play  in  the  conduction  of  an  electric  current. 
Our  closer  examination  of  the  bearing  of  the  hypothesis 
on  these  two  classes  of  phenomena  has  shown  that  the 
degree  of  dissociation  of  a  salt,  acid,  or  base  in  aqueous 
solution  can  be  estimated  in  two  ways  :  (  1  )  from  the 
osmotic  behaviour,  specially  from  the  freezing  point,  of 
the  solution;  and  (2)  from  its  conductivity.  The  vital 
question  then  arises  :  Are  the  values  of  a,  based  on 
determinations  of  the  freezing  point,  in  agreement  with 


132  PHYSICAL  CHEMISTRY 

those  based  on  measurements  of  conductivity?  The 
answer  is,  that  although  discrepancies  occur  in  individual 
cases,  the  general  parallelism  between  the  two  sets  of 
values  is  so  remarkable  as  to  furnish  a  strong  argument 
in  support  of  Arrhenius's  hypothesis.  It  was  indeed  this 
parallelism  on  which  Arrhenius  laid  the  main  emphasis 
when  the  hypothesis  was  first  brought  forward.  The 
general  agreement  between  the  values  of  a  calculated 
from  freezing  point  data  and  those  derived  from  con- 
ductivity measurements  is  illustrated  in  the  following 
table,1  which  embraces  also  certain  figures  for  the  osmotic 
activity  of  salts  based  on  de  Vries's  isotonic  coefficients. 
The  last  three  columns  of  the  table  contain  the  values  of  i 
calculated  (I.)  from  the  depression  of  the  freezing  point  ; 
(II.)  from  the  conductivity  ;  (III.)  from_de  Vries's  figures. 


Salt.                 peue  L                      n-  ™. 

KC1     .     .  .     0-14  1-82  1-86  1-81 

G4a(NO3)2  .     0-18  2-47  2-46  2  '48 

MgS04    .  .     0-38  1*20  1-35  1-25 

CaCl2  .     .  .     0-184  2-67  2-42  2'78 

K4FeCyf!.  .     0*356  ...  3-07  3-09 

More  recent  and  more  accurate  investigations  have 
shown  that  the  agreement  between  the  values  of  a  de- 
duced from  the  freezing  point  and  from  the  conductivity 
is  in  dilute  solutions  better  than  the  foregoing  table 
would  indicate.  This  contention  is  supported  by  the 
following  figures  for  potassium  nitrate  :  — 

Gram-equivalents  t  »      i    i 

per  litre.  t  =  I~  t  =  l+a 

co  from  Conductivity. 
from  Freezing  Point. 

0-02  1-90  1-91 

0-025  1-87  1-89 

0-05  1-84  1-87 

0-10  1-79  1-83 


1  van't  Hoff  and  Reicher.  Zeit.  pliysikal.  Chem.,  1889,  3,  198. 


SALT  SOLUTIONS  133 

It  ought  to  be  borne  in  mind  that  the  values  of  a 
derived  from  freezing  point  experiments  are  valid  for 
temperatures  in  the  neighbourhood  of  0°  C.,  while 
those  derived  from  electrical  measurements  are  valid 
at  18°  or  25°,  at  which  temperatures  most  determina- 
tions of  conductivity  have  been  made.  The  degree  of 
dissociation,  however,  does  not  alter  much  between  0° 
and  25°. 

Utility  of  the  Electrolytic  Dissociation  Hypothesis. — 

The  evidence  submitted  so  far  shows  that  this  hypothesis 
is  capable  of  giving  an  intelligible  interpretation  of  the 
abnormal  depression  of  the  freezing  point  on  the  one  hand, 
and  of  the  formation  and  behaviour  of  conducting  solutions 
on  the  other  hand.  The  remarkable  parallelism  between 
the  values  for  the  degree  of  dissociation  deduced  from  the 
freezing  points  of  salt  solutions  and  those  based  on  con- 
ductivity measurements  creates  a  strong  presumption  in 
favour  of  the  hypothesis,  and  it  has  therefore  been  widely 
adopted  as  a  working  theory  of  electrolytic  solutions. 
Its  utility  in  this  respect  cannot  be  denied,  and  although 
there  are  directions  in  which  apparently  the  theory 
requires  modification  or  extension,  it  has  provided  a 
satisfactory  basis  for  the  quantitative  treatment  of  the 
phenomena  exhibited  by  solutions  of  acids,  bases,  and 
salts.  Evidence  of  the  value  of  the  theory  from  this 
practical  standpoint  will  appear  later. 

It  is  perhaps  desirable  at  this  stage  to  emphasise  once 
more  the  distinction  which  the  theory  makes  between 
electrolytes  and  non- electrolytes.  Arrhenius  contends 
that  the  substances  known  as  electrolytes  are  ionised  in 
aqueous  solution,  and  that  in  virtue  of  this  ionisation 
their  solutions  conduct  the  electric  current.  The  fact 
that  a  solution  has  a  definite  conductivity  is  evidence  that 
the  dissolved  substance  is  ionised,  and  the  conductivity 


134  PHYSICAL   CHEMISTRY 

is  taken  as  a  measure  of  the  ionisation.  Non -electrolytes, 
on  the  other  hand,  are  not  ionised ;  they  have  a  normal 
effect  on  the  freezing  point  of  water,  and  their  solutions 
do  not  conduct  the  electric  current.  This  broad  dis- 
tinction between  electrolytes  and  non- electrolytes  is  not 
invalidated  by  the  fact  that  there  are  many  electrolytes 
which  are  close  to  the  border  line.  Their  aqueous  solu- 
tions are  very  feeble  conductors  of  the  electric  current, 
and  their  influence  on  the  freezing  point  of  water  is 
nearly  normal.  This  simply  means  that  the  degree  of 
dissociation  in  such  cases  is  extremely  small.  That 
there  is,  however,  a  fundamental  distinction  between 
a  typical  electrolyte,  such  as  sodium  chloride,  and 
a  typical  non-electrolyte,  such  as  sucrose,  is  clear 
from  a  consideration  of  their  osmotic  and  electrical 
behaviour. 

One  objection  which  has  been  frequently  urged  against 
the  electrolytic  dissociation  theory  may  be  considered 
here,  and  that  is  the  absence  of  a  motive  for  dissociation. 
It  is  well  known  that  the  elements  sodium  and  chlorine 
combine  with  extraordinary  vigour  to  form  sodium  chloride, 
and  that  a  very  large  amount  of  heat  is  developed 
when  the  combination  takes  place.  Yet,  according  to 
the  electrolytic  dissociation  theory,  this  compound  is  no 
sooner  dissolved  in  water  than  the  molecule  is  split 
up  into  two  ions.  This  separation  of  the  electrically 
charged  atoms  must  obviously  require  a  considerable 
amount  of  energy,  and  the  question  at  once  arises :  From 
what  source  is  this  necessary  energy  derived?  A  full 
discussion  of  the  question  cannot  be  undertaken  here, 
but  it  may  be  pointed  out  that  much  evidence  has  lately 
been  accumulated  showing  that  the  ions  are  hydrated, 
that  they  carry  about  with  them  an  envelope  of  water 
molecules.  On  the  basis  of  this  experimental  material, 
the  view  has  been  brought  forward  that  the  attraction 


SALT  SOLUTIONS  135 

of  the  ions  for  water  is  the  real  motive  for  dissociation 
in  aqueous  solution,  and  that  the  energy  necessary  for 
the  separation  of  the  ions  is  derived  from  the  heat  of 
their  combination  with  water.1 

1  See  Lowry,  Trans.   Faraday  Soo.,    1905,   1,    197;    Bousfield  and 
Lowry,  ibid.,  1907,  3,  123. 


CHAPTEE   VIII 

ELECTROLYTIC    DISSOCIATION  ;    PHYSICAL   AND 
BIOLOGICAL    APPLICATIONS 

IN  the  foregoing  chapter  the  behaviour  of  acids,  bases, 
and  salts  in  aqueous  solution  has  been  contrasted  with 
that  of  non-electrolytes,  and  it  has  been  shown  how 
the  study  of  electrolytic  solutions  led  up  to  the  theory 
of  ionic  dissociation.  The  evidence  discussed  so  far  has 
been  of  a  purely  physical  kind,  but  the  theory  has  a 
highly  important  bearing  on  many  physiological  problems 
as  well  as  on  questions  connected  with  the  general 
behaviour  of  electrolytic  solutions.  As  a  preliminary, 
therefore,  to  a  further  consideration  of  the  ionic  hypo- 
thesis in  its  various  aspects,  it  may  be  desirable  to 
mention  one  or  two  facts  which  indicate  the  part  played 
by  electrolytes  in  the  living  organism. 

The  Conductivity  of  Physiological  Fluids.— The  fluids 
which  bathe  the  tissues  of  plants  and  animals  are 
electrolytic  solutions.  They  contain,  it  is  true,  large 
quantities  of  non-electrolytic  material,  such  as  proteins, 
but  they  contain  also  appreciable  quantities  of  salts,  in 
virtue  of  which  they  are  conducting  fluids.  Blood,  for 
instance,  is  relatively  a  good  conductor,  the  conductivity 
of  the  serum  being  nearly  the  same  as  that  of  a  0'7  per 
cent,  sodium  chloride  solution.  The  figure  found  for 
the  specific  conductivity  of  ox  blood  serum  at  25°  varies 
between  0*0114  and  0'0131,  and  if  the  serum  is  diluted, 
the  specific  conductivity  diminishes  in  the  same  way 
as  that  of  an  ordinary  salt  solution.  If  the  quantity 

136 


ELECTROLYTIC  DISSOCIATION  137 

of  mixed  salts  in  1  litre  of  the  undiluted  serum  is 
taken  as  a  standard,  and  the  conductivity  of  the  diluted 
serum  is  in  each  case  referred,  not  to  1  centimetre  cube 
of  solution  but  to  this  standard  quantity  of  the  mixed 
salts,  numbers  are  obtained  which  are  analogous  to 
the  equivalent  conductivities  recorded  in  the  case  of 
an  ordinary  salt  solution,  and  which,  like  these,  increase 
with  dilution.  By  comparing  the  figure  for  the  .un- 
diluted serum  with  the  maximum  figure  obtained  on 
dilution,  it  is  possible  to  estimate  the  average  degree 
of  dissociation  of  the  salts  in  the  undiluted  serum ;  this 
turns  out  to  be  from  0*65  to  0'76.  The  serum  proteins, 
however,  which  amount  to  about  8  per  cent.,  lower  the 
conductivity  of  the  undiluted  serum  more  than  that 
of  the  diluted  serum,  in  which  their  concentration  is 
much  reduced,  so  that  the  foregoing  figure  is  certainly 
too  low.  It  is  worth  while  noting  by  the  way  that  the 
conductivity  of  defibrinated  blood  is  only  about  half 
that  of  the  corresponding  serum.  This  is  due  to  the 
fact  that  the  defibrinated  blood  contains  the  corpuscles, 
which  are  non-con  ducting  bodies,  and  diminish  the  con- 
ductivity by  obstructing  the  active  carriers  of  the  current. 
The  extent  by  which  the  conductivity  of  a  sample  of 
defibrinated  blood  is  less  than  that  of  the  corresponding 
serum  has  in  fact  been  employed  to  calculate  the  total 
volume  of  the  corpuscles  in  blood.  The  phenomenon 
is  analogous  to  the  lowering  of  the  conductivity  of  a 
sodium  chloride  solution  which  results  from  the  suspension 
of  quartz  powder  in  the  solution. 

Since  blood  and  other  physiological  fluids  are  possessed 
of  the  characteristics  of  electrolytes,  it  is  not  surprising 
that  the  replacement  of  the  fluids  which  normally  bathe 
animal  tissues  by  solutions  of  non-electrolytes  should 
result  in  very  marked  modification  of  the  activities  of 
the  tissues  so  treated.  It  has  been  found,  for  instance, 


138  PHYSICAL   CHEMISTRY 

that  if  a  frog  muscle  is  allowed  to  lie  in  isotonic  sucrose 
or  dextrose  solution  long  enough  to  extract  all  the  salts 
from  the  fluid  which  bathes  the  muscle  fibres,  then 
the  muscle  gets  into  a  condition  in  which  it  has  no 
power  either  to  transmit  or  respond  to  a  stimulus;  its 
contractility  has  disappeared.  The  power,  however,  is 
not  destroyed;  it  is  only  rendered  latent,  for  on  the 
addition  of  sodium  chloride  or  other  sodium  salts,  the 
muscle  is  again  able  to  respond  to  a  stimulus. 

While  it  is  true  that  the  greater  part  of  the  con- 
ductivity exhibited  by  physiological  fluids  is  due  to 
the  presence  of  inorganic  salts,  yet  there  are  other 
substances  present  which  are  partially  ionised,  and  which 
therefore  contribute  to  the  conductivity  of  these  fluids. 
Under  the  influence  of  enzymes  changes  take  place  in 
the  organism,  which  result  in  the  production  of  ionised 
from  non-ionised  substances.  Proteins,  for  instance,  are 
split  up  by  the  action  of  trypsin,  an  enzyme  found  in 
the  pancreatic  juice,  and  produce  peptones  and  amino- 
acids,  substances  which  are  ionised  to  a  certain  extent. 
The  course  of  such  a  protein  degradation  may  therefore 
be  followed  by  observing  the  increase  of  conductivity, 
or,  what  is  the  same  thing,  the  decrease  of  resistance. 
The  following  figures  supply  an  illustration  of  this 
phenomenon :  they  refer  to  the  action  of  trypsin  on 
a  solution  of  casein ogen : l — 


Time  in 
Minutes. 

Resistance 
in  (  >hrns. 

0 

333-0 

4 

325-5 

12 

308-2 

30 

286-1 

131 

230-0 

466 

187-4 

711 

180-1 

Bayliss,  Journ.  PhysioL,  1908,  36,  221. 


ELECTROLYTIC   DISSOCIATION  139 

The  decrease  in  viscosity  which  results  from  the  action 
of  trypsin  in  this  case  is  quite  inadequate  to  account 
for  the  increase  in  conductivity,  and  the  latter  must 
therefore  be  attributed  to  an  increase  in  the  number 
of  current  carriers,  that  is,  the  ions.  The  conductivity 
method  of  following  the  formation  of  ions  which  results 
from  protein  degradation  has  lately  been  employed  in 
comparing  the  antiseptic  value  of  disinfectants.1 

The  evidence  quoted  in  the  foregoing  paragraphs  may 
suffice  to  indicate  in  a  preliminary  way  that  in  the  processes 
associated  with  vital  activity  electrolytes  must  play  no 
inconsiderable  part.  It  is  therefore  desirable  to  con- 
sider the  characteristic  properties  of  electrolytic  solutions  in 
greater  detail  than  we  have  as  yet  done,  and  to  inquire 
how  far  the  theory  of  ionic  dissociation  is  capable  of 
interpreting  these  properties  adequately.  One  fact,  for 
instance,  which  forces  itself  on  all  who  study  the  be- 
haviour of  salt  solutions  is,  that  their  properties  are 
additive  in  character.  What  is  the  evidence  for  this 
generalisation,  and  supposing  the  evidence  to  be  satis- 
factory, how  is  it  to  be  explained  ? 

The  Additive  Character  of  the  Properties  of  Salt 
Solutions.2  Evidence  Based  on  their  Chemical  Be- 
haviour.— It  is  generally  recognised  that  the  chemical 
reactions  of  a  dissolved  salt  are  simply  the  sum  of  the 
reactions  which  are  characteristic  of  the  positive  part 
of  the  salt  and  those  which  are  characteristic  of  the 
negative  part.  The  behaviour  of  calcium  chloride,  for 
example,  in  dilute  aqueous  solution  is  not  that  of  a 
compound  which  has  its  own  individual  peculiarities; 
the  reactions  of  a  dilute  calcium  chloride  solution  are 
simply  those  which  are  common  to  calcium  salts  plus 

1  Schryver  and  Lessing,  Journ.  Soc.  Chem.  Ind.,  1909,  28,  60. 

2  The  phrase  '  gait  solutions '  is  to  be  understood  as  covering  solu- 
tions of  acids  and  bases. 

4 


140  PHYSICAL  CHEMISTRY 

those  which  are  common  to  chlorides.  The  significance 
of  this  is  apparent,  in  view  of  the  fact  that  in  a 
chemical  compound  the  characteristics  of  the  components 
cannot  as  a  rule  be  detected ;  the  properties  of  a  given 
element  are  modified  to  an  extent  which  depends  on 
the  other  element  or  elements  with  which  it  has  com- 
bined. Sulphur,  for  instance,  unites  both  with  carbon 
and  with  oxygen,  forming  carbon  disulphide  and  sulphur 
dioxide  respectively,  but  it  is  quite  impossible  to  regard 
the  properties  of  these  two  compounds  as  the  sum  of 
the  properties  of  the  components;  the  characteristics 
of  sulphur,  which  would  in  that  case  be  exhibited  by 
.both  compounds  alike,  are  conspicuously  absent. 

The  additive  character  of  the  reactions  of  dilute  salt 
solutions  is  emphasised  by  contrast  with  the  behaviour 
of  organic  substances.  The  existence  of  a  common 
atom  or  group  of  atoms  in  these  substances  cannot  be 
proved  by  the  simple  precipitation  reactions  on  which 
we  rely  for  the  recognition,  say,  of  bromides  or  sulphates 
in  aqueous  solution.  The  reactions  of  an  organic  com- 
pound, even  in  solution,  are  as  a  rule  not  resolvable 
into  the  reactions  of  the  component  atoms  or  groups. 
For  instance,  an  aqueous  solution  of  potassium  ethyl 
sulphate  is  not  precipitated  by  the  addition  of  barium 
chloride,  and  alcoholic  solutions  of  silver  nitrate  and 
phenyl  bromide  may  be  mixed  without  giving  any 
precipitate  of  silver  bromide. 

The  electrolytic  dissociation  hypothesis  supplies  an 
interpretation  of  the  additive  character  of  reactions  in 
salt  solutions.  According  to  this  hypothesis,  dilute 
solutions  of  sulphuric  acid,  copper  sulphate,  and  potassium 
sulphate  are  alike  in  this,  that  they  all  contain  large 

quantities  of  the  S04  ion,  so  that  when  barium  chloride 
is  added  to  each  of  these  solutions  the  same  result 


ELECTROLYTIC   DISSOCIATION  141 

follows.  It  is  possible  however  for  a  compound  con- 
taining the  —  S04  group,  such  as  potassium  ethyl  sulphate, 
to  dissolve  without  being  ionised,  or  to  ionise  in  a 
different  way  from  ordinary  sulphates,  and  in  such  a 
case  the  addition  of  barium  chloride  may  not  cause 
any  precipitation  whatsoever.  Similarly,  the  failure  of 
silver  nitrate  to  precipitate  phenyl  bromide  in  alcoholic 
solution  is  to  be  attributed  to  the  non-iohisation  of 
phenyl  bromide.  From  the  point  of  view,  then,  of  the 
electrolytic  dissociation  theory,  the  reactions  which  are 
so  largely  employed  in  analytical  chemistry  are  ionic 
reactions,  and  the  behaviour  of  a  salt  in  dilute  solution 
may  be  regarded  as  the  reactions  of  the  positive  ion 
plus  those  of  the  negative  ion.  The  observation 
that  a  compound  which  is  very  reactive  in  dilute 
aqueous  solution  frequently  loses  this  character  when 
dissolved  in  a  non-ionising  solvent  is  instructive  in 
this  connection.  Thus  acids  in  aqueous  solution  are 
characterised  by  their  power  of  acting  on  carbonates, 
and  yet  a  solution  of  dry  hydrogen  chloride  in  benzene 
— a  solution,  it  should  be  observed,  which  does  not 
conduct  the  electric  current — is  unable  to  attack  dry 
sodium  carbonate.1  Since  this  solution  is  a  non-con- 
ductor, we  may  conclude  that  the  dissolved  hydrogen 
chloride  is  in  the  un-dissociated  or  un-ionised  condition ; 
it  appears,  therefore,  that  the  reactions  of  hydrogen 
chloride  in  aqueous  solution  are  qiiite  different  from 
its  reactions  in  the  un-ionised  condition.  It  has  some- 
times been  suggested  that  all  instantaneous  reactions, 
such  as  those  occurring  in  the  precipitation  of  one  salt 
by  another,  are  ionic  reactions,  but  this  statement  is 
too  sweeping.  Kahlenberg2  has  found  cases  of  double 
decomposition  accompanied  by  immediate  precipitation 

1  Sec  Kahlenberg,  Journ.  Physical  Chem.,  1902,  6,  1. 
8  Loc.  cit. 


142  PHYSICAL  CHEMISTRY 

in  solutions  which  are  excellent  insulators.  Thus  a 
solution  of  dry  hydrogen  chloride  in  benzene  and  a 
solution  of  dry  ammonia  in  benzene  are  both  non- 
conductors like  benzene  itself,  and  yet,  when  mixed, 
they  give  instantly  a  white  precipitate  of  ammonium 
chloride. 

The  Colour  of  Salt  Solutions.  —  If  we  take  a  series 
of  coloured  salts  the  colour  of  which  springs  from  the 
presence  of  a  particular  metal  or  a  particular  acid 
radical,  it  is  found  that  dilute  solutions  of  the  salts 
of  each  series  have  all  the  same  colour.  This  is  the 
case  even  when  the  solid  salts  or  their  concentrated 
aqueous  solutions  differ  in  colour  ;  any  such  difference 
tends  to  disappear  with  dilution.  Concentrated  cupric 
chloride  solutions  are  green,  and  in  this  respect  differ 
from  concentrated  copper  sulphate  solutions,  which  are 
blue  ;  the  green  solutions,  however,  turn  blue  on  dilution, 
and  are  then  indistinguishable,  so  far  as  the  colour 
goes,  from  dilute  copper  sulphate  solutions.  The  colour 
of  a  cupric  salt  in  dilute  solution  is  in  fact  independent 
of  the  acid  radical,  provided  that  the  latter  itself  makes 
no  contribution  to  the  colour.  The  additive  character 
of  the  colour  of  a  salt  in  dilute  aqueous  solution  is 
brought  out  very  clearly  by  a  study  of  absorption 
spectra.  Ostwald  has  recorded  photographically  l  the 
absorption  spectra  of  solutions  of  the  permanganates  of 
lithium,  cadmium,  ammonium,  zinc,  potassium,  nickel, 
magnesium,  copper,  hydrogen,  aluminium,  sodium,  barium, 
and  cobalt  (in  all  cases  0'002  gram-equivalent  per 
litre).  The  absorption  bands  are  practically  identical 
for  all  these  solutions,  and  occupy  the  same  positions 
in  the  spectrum.  This  striking  result  strongly  supports 
the  contention  that  the  colour  of  a  dilute  salt  solution 


1  Zeit.  physikal.  Chem.,  18  J&,  9,  579 


ELECTROLYTIC   DISSOCIATION  143 

is  an  additive  property  based  on  the  independent 
contributions  made  by  the  metallic  and  acidic  parts 
of  the  salt.  An  intelligible  explanation  of  this  inde- 
pendence of  the  metallic  and  acidic  parts  of  a  salt  is 
furnished  by  the  electrolytic  dissociation  theory,  according 
to  which  a  dilute  salt  solution  is  mainly  a  mixture,  in 
electrically  equivalent  quantities,  of  the  two  ions.  The 
theory  postulates  that  the  spheres  of  influence  of  these 
ions  are  distinct,  and  that  in  regard  to  colour  as  well 
as  chemical  reactivity,  each  ion  makes  its  characteristic 
contribution  to  the  properties  of  the  solution. 

Ionic  Conductivity. — Evidence  of  a  more  definitely 
quantitative  kind  in  favour  of  the  view  that  the  metallic 
and  acidic  parts  of  a  salt  are  to  a  large  extent  inde- 
pendent of  each  other  in  dilute  solution  is  obtained 
by  considering  the  way  in  which  the  value  of  the 
equivalent  conductivity  varies  from  one  salt  to  another. 
Suppose  that  for  this  purpose  we  deal  with  the  figures 
recorded  in  the  following  table;  they  represent  the 
equivalent  conductivities  found  for  half-a-dozen  alkali 
salts  at  18°  in  0*0001  normal  concentration:1 — 

Chloride.  Nitrate. 

Potassium  .     .     .     .     129*05  125-49 

Sodium 108-06  104'53 

Lithium 98'06  94-38 

A  glance  at  these  figures  will  show  that  XKCI  —  ^NaCi 
=  20'99,  and  that  AKN03  —  \NaNo3  =  20*96,  practically  the 
same  figure.  Further,  XKci  —  ^LICI  =  30-99,  while  XKNOS 
31'll,  practically  the  same  figure.  Again,  XKci 
3-56,  \Naci  —  ^NaNos  =  3*53,  and  ALici  —  XLING., 
=  3*68.  Expressed  in  words,  these  figures  mean  that  the 
change  in  the  value  of  the  equivalent  conductivity  produced 

1  Kohlvausch  and  Maltby,   Sitzungsber.  Tc.  ATcad.   Wiss.  Berlin,  1899, 
665. 


144  PHYSICAL   CHEMISTRY 

by  substituting  a  sodium  salt  or  a  lithium  salt  for  a 
potassium  salt  is  the  same  whether  the  salt  is  a  chloride 
or  a  nitrate ;  that  is,  the  metallic  part  of  the  salt 
makes  a  contribution  to  the  conductivity  which  is  in- 
dependent of  the  acidic  radical  with  which  it  is  associated. 
The  values  of  the  last  three  differences  show  similarly 
that  the  substitution  of  a  nitrate  for  a  chloride  of  equal 
concentration  leads  to  a  decrease  of  X,  which  is  the 
same  whether  the  metallic  part  of  the  salt  is  potassium, 
sodium,  or  lithium.  Similar  relationships  would  be  found 
to  exist  if  we  dealt  with  the  values  of  X^,  obtained  by 
extrapolation,  instead  of  the  values  of  X  for  O'OOOl 
normal  solutions,  and  we  may  therefore  conclude  that 
the  contribution  which  an  ion  makes  to  the  equivalent 
conductivity  of  a  highly  diluted  solution  is  independent 
of  the  other  ion  with  which  it  is  associated.  Kohlrausch, 
who  first  detected  the  additive  character  of  the  con- 
ductivity of  a  highly  diluted  salt  solution,  expresses 
the  independence  of  the  ions  in  this  respect  by  the 
equation  X^  =  u  -f  v,  where  u  and  v  are  the  contributions 
which  the  cation  and  anion  respectively  make  to  the 
equivalent  conductivity  at  infinite  dilution.  This  equation 
is  the  expression  of  what  is  generally  known  as  Kohl- 
rausch's  Law  of  the  Independent  Migration  of  the 
Ions,  and  the  terms  u  and  v  which  appear  in  the 
equation  are  described  as  ionic  conductivities.  The  value 
of  u  for  a  given  cation  remains  the  same  for  all  salts 
which  contain  this  cation,  just  as  the  value  of  v  for 
a  given  anion  remains  the  same  whatever  be  the  salt 
of  which  it  forms  part.  The  actual  numerical  values 
of  u  and  v  cannot  however  be  obtained  until  some  other 
equation  is  available  which  involves  these  quantities. 

The  numbers  recorded  in  the  last  table  show  very 
clearly  that  the  contribution  made  to  the  conductivity 
by  the  lithium  ion  is  less  than  that  made  by  the  sodium 


ELECTROLYTIC   DISSOCIATION  145 

ion,  and  this  again  is  less  than  the  contribution  made 
by  the  potassium  ion.  In  view  of  this  the  question 
at  once  suggests  itself:  Why  should  one  ion  contribute 
more  than  another  to  the  conductivity  of  a  solution? 
If,  in  accordance  with  the  theory  of  electrolytic  dis- 
sociation, we  conceive  the  passage  of  a  current  through 
an  electrolyte  as  consisting  in  the  movement  of  elec- 
trically charged  material  particles,  we  might  regard  the 
superior  efficiency  of  a  given  ion  in  the  conduction 
of  the  current  as  due  either  to  its  carrying  a  greater 
charge,  or  to  its  moving  more  rapidly  than  other  ions 
under  the  same  conditions.  The  first  explanation  cannot 
be  maintained,  for  Faraday  has  shown  that  the  quantities 
of  different  ions  liberated  during  electrolysis  by  a  given 
current  are  in  the  ratio  of  their  chemical  equivalents ; 
that  is,  with  a  gram-equivalent  of  each  ion  there  is 
associated  the  same  definite  quantity  of  electricity.  All 
univalent  ions — for  example,  K',  Na",  Cl',  N03',  NH4* — 
must  therefore  carry  the  same  charge.  We  are  driven 
accordingly  to  the  second  possible  explanation  of  the  differ- 
ence in  the  contributions  made  by  various  ions  to  the  con- 
ductivity, namely,  that,  exposed  to  the  same  electrical 
forces,  different  ions  have  different  mobilities:  one  ion 
may  be  faster  or  slower  than  another  ion.  The  accept- 
ance of  this  view  involves  certain  conclusions  as  to 
changes  of  concentration  which  must  accompany  the 
process  of  electrolysis.  We  shall  first  deduce  these 
conclusions,  and  then  compare  them  with  the  results  of 
experimental  work. 

The  assumption  that  the  contribution  which  an  ion 
makes  to  the  equivalent  conductivity  depends  on  its 
mobility  may  be  expressed  more  definitely  by  the  equation 

u     speed  of  cation  -,    • ,     •  i  ,  •>          .  <,    . , 

-  =  --—  — = — - — ,    and   it  is   easy  to    show    that   it    the 
v      speed  of  anion 

ions  of  a  salt  move  at  different  rates,  the  fall  of  con- 


146 


PHYSICAL   CHEMISTRY 


centration  round  the  anode  due  to  electrolysis  is  different 
from  the  fall  of  concentration  round  the  cathode. 
Suppose  that  the  condition  of  an  electrolytic  solution 
before  electrolysis  commences  is  represented  diagram- 
matically,  as  in  Fig.  17.  Between  the  anode  A  and 
the  cathode  C  there  is,  we  may  suppose,  only  a  limited 
number  of  fully  ionised  molecules.  The  electrolytic 


FIG.  17. 

cell  may  be  conceived  as  divided  into  three  parts, 
a  compartment  round  the  anode  and  one  round  the 
cathode,  each  containing  six  fully  ionised  molecules, 
as  well  as  an  intermediate  compartment  containing  four 
fully  ionised  molecules.  The  compartments  are  separated 
from  one  another  by  the  porous  septa  SS. 

Suppose,  to  begin  with,  that  the  positive  and  negative 
ions  move  at  the  same  rate.  If  a  current  is  passed 
just  so  long  that  two  cations  cross  each  of  the  septa  SS 
from  left  to  right,  then  in  this  time  two  anions  will 
have  crossed  the  septa  from  right  to  left,  and  the  position 
of  matters  will  be  as  represented  in  Fig.  18.  In  the 

s  s 

©©©©©©©©©©©©©©©©I 
©©©©©©©©©©©©©©©© 

FIG.  18. 

intermediate  compartment  there  will  still  be  four  mole- 
cules as  before  the  electrolysis;  the  concentration  there 
is  unaltered.  The  isolated  ions  are  those  which  have 
been  liberated  at  the  electrodes  during  the  passage  of 


ELECTROLYTIC   DISSOCIATION  147 

the  current:  the  number  of  these  liberated  ions  is  the 
same  at  each  electrode,  as  required  by  Faraday's  law. 
In  the  solution  round  the  anode  there  are  now  four 
molecules — a  loss  of  two  molecules;  in  the  cathode 
compartment  there  are  four  molecules  left — likewise  a 
loss  of  two  molecules.  Hence,  when  the  ions  move  at 
the  same  rate,  the  fall  of  concentration  round  the  anode 
is  equal  to  the  fall  of  concentration  round  the  cathode. 
Suppose  next  that  the  speed  of  the  cation  is  twice  as 
great  as  that  of  the  anion,  and  that  the  current  passes 
just  so  long  that  two  cations  pass  across  each  of  the 
septa  SS  from  left  to  right ;  in  this  time  one  anion 
will  pass  across  each  septum  from  right  to  left,  and  the 
position  of  matters  will  then  be  as  represented  in  Fig.  19. 

s  s 

©©©©©©©©©©©<©©©©© 
©©©©©©©©©e©©©©©© 

FIG.  19. 

As  before,  the  concentration  in  the  intermediate  com- 
partment is  unaltered,  while  three  ions  have  been 
liberated  at  each  electrode.  The  number  of  molecules 
left  in  the  anode  compartment  is  now  four — a  loss  of 
two;  the  number  of  molecules  left  in  the  cathode  com- 
partment is  five — a  loss  of  one.  We  have  therefore 

Fall  of  concentration  round  anode    2 speed  of  cation 

Fall  of  concentration  round  cathode      1      speed  of  anion 

This  line  of  argument  might  be  extended  to  cover 
other  speed  ratios,  and'  a  similar  conclusion  would  be 
reached.  On  the  basis,  therefore,  of  the  view  that  dif- 
ferent ions  make  contributions  to  the  equivalent  con- 
ductivity in  proportion  to  their  rates  of  migration 


148  PHYSICAL   CHEMISTRY 

under  the  action  of  the  same  electrical  force,  we  have 

u  _  speed   of   cation  _    fall  of  concentration  round  anode 

v  ~~  speed  of  anion  ~~  fall  of  concentration  round  cathode'    Pr( 

vided  that  in  any  experiment  carried  out  in  order  to 
determine  the  relative  speed  of  the  ions  there  is  an 
intermediate  zone  of  the  electrolyte  in  which  no  change 
of  concentration  has  taken  place.  If  we  adopt  the  view 
that  during  the  electrolysis  of  a  salt  solution  the  ions 
are  moving  at  different  speeds,  then  it  is  obvious  that 
of  the  electricity  which  is  transported  across  any  given 
section  of  the  electrolyte,  a  greater  fraction  will  be 
carried  by  one  ion  than  by  the  other.  If,  for  instance, 
the  cation  moves  twice  as  fast  as  the  anion,  then  two 
cations  will  cross  a  given  section  of  the  electrolyte  from 
left  to  right,  while  one  anion  is  crossing  the  same 
section  from  right  to  left  ;  since  the  ions  carry  equal 
charges,  this  means  that  the  quantity  of  positive  elec- 
tricity transported  across  the  section  is  twice  as  great 
as  the  quantity  of  negative  electricity.  To  put  it  gene- 
rally, let  us  suppose  that  of  the  total  transported  elec- 
tricity the  fraction  n  is  carried  by  the  anions  and  the 
fraction  1  —  n  by  the  cations  ;  then 

l-n_w_  fall  of  concentration  at  anode 
n    ~  v  ~  fall  of  concentration  at  cathode* 

Now  there  is  a  well-known  algebraic  theorem  which 
states  that  if  -  =  ,  then  —  =  j  if  this  theorem  is 


applied  to  the  foregoing  equations,  it  is  easily  shown  that 
fall  of  concentration  at  anode 


1-71  = 

and  n=-^—  = 


u  +  v        total  fall  of  concentration    * 

fall  of  concentration  at  cathode 
total  fall  of  concentration 


Hittorf s  Work. — So  far  we  have  simply  attempted 
to  deduce  the  conclusions  that  follow  from  the  assump- 
tion of  different  ionic  velocities,  and  we  may  now  ask. 


ELECTROLYTIC   DISSOCIATION  149 

Do  changes  of  concentration  occur  round  the  electrodes 
during  electrolysis,  and  if  so,  is  the  fall  of  concentration 
at  one  electrode  in  some  cases  different  from  that  at 
the  other  electrode?  These  questions  were  answered 
long  ago  in  the  affirmative  by  the  classical  work  of 
Hittorf,  who  determined  the  values  of  n  and  1  —  n,  the 
transport  or  migration  numbers  as  they  are  called, 
for  various  anions  and  cations.  A  particular  example 
may  perhaps  be  quoted  to  show  the  sort  of  experi- 
mental data  which  Hittorf  obtained,  and  the  way  in 
which  he  employed  these  data  to  calculate  the  transport 
number.  An  electrolytic  cell  containing  a  solution  of 
copper  sulphate  was  put  in  series  with  one  containing 
a  solution  of  silver  nitrate.  After  a  current  had  been 
passed  for  some  time,  it  was  found  that  1*008  gram  of 
silver  had  been  deposited  on  the  cathode  of  the  silver 
nitrate  cell.  According  to  Faraday's  law,  this  amount 
of  silver  must  be  equivalent  to  the  copper  deposited 
on  the  cathode  of  the  copper  sulphate  cell;  this  weight 

of  copper  must  therefore  be  1 -008  X~j|  =  0'2968  gram, 

a  figure  which  is  a  measure,  in  terms  of  copper,  of  the 
total  loss  of  concentration  in  the  copper  sulphate  cell. 
Before  electrolysis  the  solution  round  the  cathode  con- 
tained, as  shown  by  analysis,  an  amount  of  copper 
sulphate  equivalent  to  2*8543  grams  of  copper  oxide : 
after  electrolysis  the  cathode  solution  gave  on  analysis 
2*5897  grams  of  copper  oxide.  Electrolysis  has  resulted 
therefore  in  a  fall  of  concentration  at  the  cathode  re- 
presented by  0*2646  gram  CuO  or  0*2114  gram  Cu. 
This  loss,  however,  is  less  than  the  weight  of  copper 
which  has  been  deposited  on  the  cathode  out  of  the 
surrounding  solution,  namely,  0*2968  gram,  and  it  is 
therefore  obvious  that  the  difference,  0*2968-0*2114 
=  0*0854  gram,  must  have  migrated  from  the  anode  com- 


150  PHYSICAL  CHEMISTRY 

partment  into  the  cathode  compartment.  The  figure 
0-0854  represents,  in  terms  of  copper,  the  fall  of  con- 
centration round  the  anode,  and  we  have  accordingly 
.,  fall  of  concentration  at  anode  0-0854  A  000  -,  .  , 

"i  of  concentration-  =  6^2968  =  °"288>  whlch 


is  therefore  the  transport  number  for  the  copper  ion 
in  this  solution.  The  transport  number  for  the  sulphate 
ion  is  0*712,  and  a  comparison  of  these  figures  shows 
that  of  the  total  electricity  transported  across  any  section 
of  the  electrolyte  about  seven-tenths  is  carried  by  the 
negative  ions. 

Numerical  Values  for  Ionic  Conductivity.  —  From  the 
work  of  Hittorf  and  others  who  have  followed  him,  we 
know  then  the  ratio  of  the  contributions  which  the  ions 
of  an  electrolyte  make  to  the  equivalent  conductivity. 
The  value  of  this  ratio  may  not  be  the  same  in  con- 
centrated and  in  dilute  solutions  of  the  electrolyte,  but 
it  is  found  on  investigation  that  after  a  certain  stage 
of  dilution  no  further  change  in  the  value  of  the  ratio 
takes  place.  As  an  illustration  of  this  we  may  take 
the  following  figures  obtained  by  Hittorf  for  the  tran- 
sport number  (l  —  n)  of  silver  in  silver  nitrate  solutions 
of  different  concentration  :  — 

Weight  of  Water  to  , 

1  gram  AgN03. 

2-48  ......  0-532 

2-73  ......  0-522 

5-18  ......  0-505 

10-38  ......  0-490 

14-5  ......  0-475 

49-4  ......  0-474 

247-3  ......  0-476 

These  figures  show  that  the  transport  number  for 
silver  in  dilute  solutions  is  0-475,  and  that  this  value 
does  not  alter  over  a  considerable  range  of  concentration. 


ELECTROLYTIC   DISSOCIATION  151 

So  for  other  ions  values  of  the  transport  numbers  are 
obtained  which  are  valid  for  highly  diluted  solutions, 
and  which  can  be  used  in  the  following  way  to  calculate 
ionic  conductivities.  We  have  seen  that  X^  =  u  +  v, 

l  —  n  =  ^-,  and  n  =  ^r^]  hence  it  follows  that  u  =  (1  —  n)\x , 

and  'y  =  ?iX00.  The  value  of  X^  for  a  salt  is  ascertained, 
as  already  shown,  by  extrapolating  from  the  actually 
observed  figures  for  X,  while  the  values  of  n  and 
1  —  Ti  are  given  by  Hittorf's  work.  As  an  example 
of  the  way  in  which  ionic  conductivities  are  calculated, 
the  case  of  potassium  chloride  may  be  taken.  For  this 
salt  X^  at  18°  =  129*9,  while  the  transport  number  for 
chlorine  is  0'503.  We  have  then  <^  =  0*497  X  129*9  =»64*6, 
and  v  =  0*503  x  129*9  =  65-3  ;  that  is,  the  ionic  conduc- 
tivity of  potassium  at  18°  is  6-4*6,  and  the  ionic  con- 
ductivity of  chlorine  is  65*3  at  the  same  temperature. 

In  a  similar  manner,  by  combining  the  values  of  n, 
l  —  ?i,  and  X^for  any  electrolyte  it  is  possible  to  calculate 
other  ionic  conductivities.  It  is  noteworthy,  however, 
that  when  one  ionic  conductivity  has  been  evaluated,  all 
others  can  be  calculated  from  it  by  means  of  the  formula 
\^=u  +  v,  without  any  further  determination  of  trans- 
port numbers.  Suppose,  for  instance,  that  on  the  basis 
of  the  value  0*503  for  the  transport  number  of  chlorine 
in  potassium  chloride  the  ionic  conductivity  of  chlorine 
at  18°  has  been  found  to  be  65*3,  as  just  shown.  Then 
since  X  for  sodium  chloride  at  18°  has  been  found  to 

CO 

be  108*8,  and  since,  according  to  Kohlrausch's  law  of  the 
independent  migration  of  the  ions,  X^for  NaCl  =  wNa  +  Vcb 
we  have  1 08*8  =  u$a  +  65*3,  whence  WNa  =  43*5. 

The  following  table  records  the  values  of  the  con- 
ductivity at  1 8°  for  various  ions  : — 


152  PHYSICAL   CHEMISTRY 


Cations. 

Anions. 

H     . 

.     .      .318 

OH 

. 

174 

Li    . 

.     .     .     33-4 

Cl 

. 

65-3 

Na 

.     .     .     43'5 

I 

66-4 

K     . 

.     .     .     64-6 

N03 

. 

61-8 

NH4 

.     .     .     64-4 

CH3. 

COO.    . 

337 

Ag  . 

.     .     .     54-0 

These  figures,  it  should  be  noted,  are  based  on  the 
investigation  of  electrolytes  for  which  X^  can  be  deter- 
mined by  extrapolation  from  the  measured  values  of  X. 
So  soon,  however,  as  the  values  of  u  and  v  have  been 
ascertained  for  various  ions  it  becomes  possible  to  calcu- 
late the  value  of  X^  for  electrolytes  where  an  extra- 
polation cannot  be  made.  Acetic  acid  supplies  an  instance 
of  this.  A  glance  at  the  figures  for  acetic  acid  recorded 
in  the  table  on  p.  129  shows  that  even  at  the  highest 
dilutions  the  value  of  X  is  still  increasing  so  rapidly  that 
an  extrapolation  is  not  permissible.  But  if  Kohlrausch's 
law  is  valid  for  acetic  acid  at  infinite  dilution  as  it  is 
for  other  electrolytes,  then  X^  =w>E.  +  Vjie,  where  u#  is  the 
ionic  conductivity  of  hydrogen,  and  VA.C  is  the  ionic  con- 
ductivity of  the  acetate  radical.  The  values  of  WH  ai*d  vAc 
have  been  ascertained  by  a  study  of  strong  acids  and  of 
alkali  acetates,  and  are  recorded  in  the  table  of  ionic  con- 
ductivities. Hence  for  acetic  acid  X^  =  318  +  33*7  =  351-7, 
a  figure  which  has  been  quoted  already  on  p.  130. 

Actual    Yelocity    of    Migration    of   the    Ions. — The 

method  employed  in  deducing  the  values  of  the  ionic  con- 
ductivities is  based  on  the  view  that  electrolysis  consists 
in  a  streaming  of  positively  charged  ions  in  one  direction 
and  of  negatively  charged  ions  in  the  opposite  direction, 
that  the  positive  and  negative  ions  may  move  at  different 
rates,  and  that  to  this  cause  is  due  the  difference  in 
the  contributions  which  the  two  ions  of  an  electrolyte 
make  to  the  equivalent  conductivity.  This  view  is  con- 


ELECTROLYTIC   DISSOCIATION  153 

firmed  by  the  concentration  changes  which  do  occur  during 
electrolysis,  and  by  the  relative  magnitude  of  these  changes 
round  anode  and  cathode  respectively.  The  values  of  u 
and  v  already  quoted  give,  however,  no  direct  information 
as  to  the  actual  speed  at  which  the  ions  move  under  the 
action  of  a  given  electromotive  force.  They  are  measured 
in  the  same  units  as  the  equivalent  conductivity,  and 
enable  us  in  the  first  place  to  deduce  only  the  relative 
speeds  of  the  two  ions  of  an  electrolyte  under  the  same 
conditions.  The  actual  speed  of  any  particular  ion  will 
of  course  depend  on  the  magnitude  of  the  electric  force 
which  is  acting  on  it,  in  other  words,  on  the  steepness 
of  the  potential  gradient  between  the  two  electrodes. 

It  is,  however,  possible  to  calculate  from  the  ascertained 
values  of  ionic  conductivity  the  actual  rates  at  which  the 
ions  move  when  the  fall  of  potential  through  the  elec- 
trolyte has  some  definite  value,  say  1  volt  per  cm.  The 
details  of  this  calculation  cannot  be  given  here,  but  the 
results  may  be  illustrated  by  the  following  figures.  Pro- 
vided that  the  fall  of  potential  in  the  electrolyte  is  1  volt 
per  cm.,  the  hydrogen  ion  moves  at  the  rate  of  0-0033 
cm.  per  second,  the  hydroxyl  ion  0*0018  cm.  per  second? 
and  the  potassium  ion  0*00067  cm.  per  second.  If  in 
some  particular  case  the  fall  of  potential  were  10  volts 
per  cm.,  then  the  rates  at  which  the  ions  move  would  be 
ten  times  as  great. 

Not  only  is  it  possible  to  calculate  the  actual  velocity 
of  the  ions ;  it  can  be  determined  by  direct  observation. 
The  way  in  which  this  is  possible  is  illustrated  by  the 
following  experiment,  first  suggested  by  Nernst.  A 
glass  tube,  about  1  mm.  bore,  is  sealed  at  one  end  to 
a  small  tap  funnel  and  at  the  other  to  a  U  tube,  each 
limb  of  which  is  5-8  mm.  diameter.  The  capillary  tube 
is  then  bent  as  shown  in  Fig.  20.  A  dilute  solution 
of  potassium  permanganate  (O'OOS  normal  relatively  to 


154 


PHYSICAL  CHEMISTRY 


potassium),  to  which  5-10  per  cent,  'of  urea  has  been 
added  in  order  to  increase  its  density,  is  poured  into  the 
funnel,  and  the  tap  is  opened  until  the  capillary  tube 
is  filled  as  far  as  its  junction  with  the  U  tube.  The  tap  is 
then  closed,  and  the  U  tube  is  half  or  two-thirds  filled  with 
a  0*003  normal  solution  of  potassium  nitrate.  The  stop- 
cock is  again  carefully  turned  on,  and 
the  permanganate  solution  is  allowed 
to  occupy  the  bottom  of  the  U  tube 
slowly,  pushing  the  potassium  nitrate 
solution  before  it  into  each  limb. 
When  the  U  tube  is  completely  full  the 
stopcock  is  finally  turned  off.  We  thus 
obtain  a  column  of  potassium  perman- 
ganate solution  isolated  between  two 
columns  of  potassium  nitrate  solution. 
Two  platinum  wires  connected  with 
the  terminals  of  a  powerful  battery, 
or  say  a  100-volt  lighting  circuit,  are 
dipped  in  the  solution  at  the  top  of 
each  limb,  the  positive  wire  being 
placed  in  the  right-hand  limb.  After 
the  current  has  been  running  for  a 
short  time  it  is  seen  that  the  boundary 
between  coloured  and  colourless  solu- 
tion  is  higher  in  the  right  limb 
than  in  the  left ;  that  is,  the  per- 
manganate ion  which  is  responsible 
for  the  colour  of  the  permanganate 
solution  has  visibly  advanced  towards  the  anode.  If  the 
advance  of  the  boundary  is  measured,  and  if  the  potential 
difference  between  the  electrodes,  as  well  as  their  distance 
apart,  is  known,  we  may  estimate  the  actual  rate  at 
which  the  permanganate  ion  .would  migrate  if  the  fall 
of  potential  were  1  volt  per  cm. 


FIG.  20. 


ELECTROLYTIC   DISSOCIATION  X55 

The  correctness  of  this  estimate  depends  on  whether 
the  fall  of  potential  is  regular  throughout  the  whole 
column  of  electrolyte  between  the  electrodes.  This  would 
be  the  case  only  if  the  specific  conductivity  of  the  per- 
manganate solution  were  the  same  as  that  of  the  potas- 
sium nitrate  solution.  It  is  evident,  therefore,  that  any 
determination  of  the  rate  at  which  an  ion  moves  involves 
a  knowledge  not  only  of  the  distance  covered,  but  also 
of  the  exact  potential  gradient.  A  discussion  of  the 
means  adopted  to  ascertain  the  potential  gradient,  and 
of  the  conditions  necessary  to  secure  a  sharp  boundary 
between  two  solutions  during  electrolysis,  is  beyond  the 
scope  of  this  volume,  but  it  may  be  mentioned  that  the 
advance  of  a  boundary  even  between  two  colourless  solu- 
tions can  be  followed  by  a  method  depending  on  the 
difference  in  refractive  index.1 

Ionic  Conductivity  and  Hydration. — Consideration  of 
the  numerical  values  of  the  ionic  conductivity  raises  a 
point  of  great  interest  in  connection  with  the  theory 
of  solutions.  In  the  group  of  alkali  metals,  as  recorded 
on  p.  152,  %Li  — 33*4,  /z%a  =  43'5,  and  %K  =  64*6  ;  the 
lightest  metal  furnishes,  therefore,  the  most  sluggish  ion 
of  the  three,  and  the  heaviest  metal  yields  the  most 
speedy  ion.  This  curious  result  is  now  generally  attri- 
buted to  the  different  hydration  of  the  ions.2  It  is 
supposed  that  of  the  three  the  lithium  ion  is  hydrated 
to  the  greatest  extent,  and  that  the  size  of  the  water 
'  envelope,'  of  which  the  lithium  ion  is  the  nucleus,  is 
responsible  for  the  greater  friction  experienced  by  it  in 
passing  through  the  water,  and  therefore  for  its  smaller 
mobility.  The  potassium  ion,  on  the  other  hand,  is  pre- 

1  Steele,  Journ.  Chcm.  Soc  ,  1901,  79,  414. 

2  See  Kohlrausch,  Proc.  Roy,  Soc.,  1903,  71,  338;    Bousfield,  Proc. 
Roy.  Soc.,  1905,  74,  5G3;  Phil.  Trans.,  A,  190(5,  206,  101  ;  Senter,  Science 
Progress,  Jan.  1907. 


156  PHYSICAL  CHEMISTRY 

sumably  hydrated  to  a  less  extent  than  either  the  sodium 
or  the  lithium  ion.  It  is  further  noteworthy  that  for  the 
three  ions  already  mentioned  the  temperature  coefficient 
of  the  mobility  is  greatest  for  the  lithium  ion  and 
smallest  for  the  potassium  ion.  This  observation  is  at 
least  in  harmony  with  the  view  that  the  relative  hydration 
is  as  suggested,  for  rise  of  temperature  is  bound  to 
favour  the  breaking  down  of  the  hydrates,  and 
the  effect  of  a  rise  of  temperature  would  probably  be 
most  marked  in  the  case  of  the  ion  which  is  most 
highly  hydrated. 

The  view  that  the  ions  of  an  electrolyte  are  hydrated 
finds  support  in  the  observation  that  the  temperature 
coefficient  of  the  conductivity  of  a  dilute  solution  is 
practically  the  same  as  the  temperature  coefficient  of 

the  fluidity   of  water   ( fluidity  =  —. n— J.     This   seems 

to  show  that  the  resistance  which  the  ions  experi- 
ence in  their  movements  is  the  frictional  resistance 
of  the  solvent,  a  result  which  becomes  intelligible  if  it 
is  supposed  that  each  ion  carries  a  water  envelope 
along  with  it. 

Ionic  Conductivity  and  the  Diffusion  of  Electro- 
lytes.— The  difference  in  the  contributions  which 
various  ions  make  to  the  equivalent  conductivity  of 
an  electrolyte  has  been  attributed  to  the  difference  in 
their  speeds.  The  figures  recorded  in  the  table  on  p.  152 
are  therefore  a  measure  of  the  speeds  at  which  the 
ions  move  under  the  action  of  a  given  electromotive 
force ;  they  are  proportional  to  the  '  mobility '  of  the 
ions.  Now  the  mobility  of  an  ion  will  come  into  play 
not  only  when  it  is  in  an  electric  field,  but  when  it 
is  involved  in  a  concentration  gradient,  that  is,  when 
the  salt  of  which  it  forms  part  is  diffusing  from  places 
of  high  concentration  to  places  of  low  concentration. 


ELECTROLYTIC   DISSOCIATION  157 

In  the  case  of  hydrochloric  acid,  for  instance,  the  fact 
that  the  mobility  of  the  hydrogen  ion  is  about  five 
times  that  of  the  chlorine  ion  must  have  a  direct  bear- 
ing on  the  rate  of  diffusion. 

Suppose  that  a  solution  of  hydrochloric  xicid  is  in 
contact  with  pure  water.  Diffusion  occurs,  and  it 
might  be  thought  in  view  of  their  relative  mobilities 
that  the  hydrogen  ions  would  soon  outstrip  the  slower 
chlorine  ions.  A  little  reflection,  however,  shows  that 
such  a  separation  of  ions  cannot  take  place  except  to 
an  infinitesimal  extent.  In  consequence  of  the  greater 
mobility  of  hydrogen,  the  front  rank  of  the  diffusing 
acid  will  consist  of  positive  hydrogen  ions,  while  behind 
these  there  will  be  an  excess  of  negative  ions.  Electro- 
static forces  are  thus  called  into  action,  which  prevent 
anything  more  than  an  infinitesimal  separation,  and  which 
have  the  effect  of  retarding  the  advance  of  the  hydrogen 
ions  and  accelerating  that  of  the  chlorine  ions.  The 
net  result  is  that  the  acid  diffuses  as  a  whole  without 
any  measurable  separation  of  hydrogen  and  chlorine, 
the  different  natural  mobilities  of  the  two  ions  being 
compensated  by  the  action  of  the  electrostatic  forces. 
It  is  evident,  however,  that  the  rates  of  diffusion  of 
different  chlorides  will  depend  on  the  mobility  of  the 
positive  ion,  on  its  ability  to  push  on  in  front  and  so 
accelerate  the  advance  of  the  chlorine  ion.  We  may 
therefore  expect  that  when  various  chlorides  are  arranged 
in  order  according  to  their  rates  of  diffusion  in  aqueous 
solution,  the  order  will  be  the  same  as  that  of  the 
conductivities  of  the  positive  ions ;  similarly,  we  may 
expect  that  when  various  sodium  salts  are  arranged 
according  to  their  rates  of  diffusion  in  aqueous  solution, 
the  order  will  be  the  same  as  that  of  the  conductivities 
of  the  negative  ions.  These  expectations  are  borne 
out  by  the  figures  in  the  following  tables,  which  give 


158  PHYSICAL   CHEMISTRY 

the  diffusion  coefficients  of  various  chlorides  and  various 
sodium  salts  at  18°  : — 


Diffusion 
Coefficient. 

HOI  .  .  .  2-30 

KC1  .  .  .  1-46 

NaCl  .  .  .  1-14 

LiCl  1-00 


Diffusion 
Coefficient. 

NaOH  .     .  .  1-40 

NaCl      .    .  .  1-14 

NaNO3.     .  .  1-03 

NaCH3COO  .  0-78 


Reference  to  the  table  of  ionic  conductivities  on  p.  152 
will  show  that  in  regard  to  mobility,  H'>K*>]STa'>Li', 
and  that  OH'  >  Cl'  >  N03'  >  CH3CO(y. 

The  difference  in  mobility  of  various  ions,  then,  is 
modified,  so  far  as  diffusion  is  concerned,  by  the  electro- 
static attraction  between  the  ions,  and  gives  rise  to  a 
difference  of  potential  at  the  common  surface  (1)  of 
salt  solution  and  water,  (2)  of  differently  concentrated 
solutions  of  the  same  salt,  or  (3)  of  solutions  of  different 
salts.  It  is  in  this  direction  that  we  must  seek  for 
an  explanation  of  the  electrical  effects  which,  as  found 
by  physiologists,  so  frequently  accompany  vital  activity. 
Differences  of  electrical  potential  in  the  tissues  are 
probably  due  to  a  separation  (infinitesimal  in  extent) 
of  the  positive  and  negative  ions  of  the  electrolytes 
which  bathe  these  tissues. 

It  will  be  apparent  from  the  foregoing  that  the 
positive  and  negative  ions  of  an  electrolyte  are  not 
absolutely  independent.  The  charges  which  the  ions 
carry  are  responsible  for  the  intervention  of  electro- 
static forces,  and  these  limit  the  independence  of  the 
ions,  so  far  at  least  as  their  separation  is  concerned. 
Another  case  in  which  the  factor  of  electrostatic  attrac- 
tion between  the  ions  has  a  definite  bearing  is  the 
problem  of  the  permeability  of  living  membranes  to 
electrolytes.  So  far  as  reference  has  been  made  to 
this  problem  in  the  present  volume,  the  behaviour  of  salts 


ELECTROLYTIC   DISSOCIATION  159 

only  as  indivisible  units  has  been  considered.  We  have 
however  now  adopted  the  view  that  salts  are  more  or  less 
ionised  in  aqueous  solution,  and  that  the  ions  are  in 
many  respects  independent  of  each  other.  The  questions 
then  naturally  arise :  Is  it  not  possible  that  the  two 
ions  of  a  salt  are  characterised  by  a  different  power 
of  penetrating  the  living  membrane  ?  If  so,  what  would 
be  the  result  if  a  solution  of  the  salt  were  separated 
from  pure  water  by  such  a  membrane  ?  If  we  assume 
for  the  moment  that  the  ions  of  a  salt  do  differ  in  their 
power  of  penetration,  and,  taking  an  extreme  case,  we 
suppose  that  the  membrane  is  permeable  to  the  anion 
but  impermeable  to  the  cation,  then  a  little  consideration 
shows  that  the  salt  as  a  whole  cannot  penetrate  the 
membrane.  For  the  passage  of  the  anions  through  the 
membrane  would  mean  a  separation  of  the  ions;  this, 
as  has  been  already  shown,  is  opposed  by  the  electrostatic 
forces,  and  can  take  place  to  an  extent  which,  so  far 
as  analytical  methods  of  detection  go,  is  absolutely 
negligible  ;  the  membrane  would  be  practically  imper- 
meable to  the  salt.  /It  would,  however,  be  the  seat 
of  a  potential  difference  originating  in  the  same  manner 
as  the  potential  difference  at  the  common  surface  of 
salt  solution  and  water,  and  the  possibility  of  electrical 
effects  arising  in  this  way  at  the  surface  of  a  membrane 
bathed  by  an  electrolyte  has  an  important  bearing  on 
the  problems  of  electro-physiology. y 

In  the  case  of  the  salt  just  described  the  anions  are 
prevented  from  passing  through  the  membrane  by  the 
inability  of  their  positive  partners.  Actual  transport 
of  these  anions  through  the  membrane  would  be  rendered 
possible  however  either  (1)  by  adding  to  the  salt  solution 
another  electrolyte  the  cation  of  which  is  able  to  pene- 
trate the  membrane,  or  (2)  by  adding  to  the  water  on 
the  further  side  a  salt  for  the  anion  of  which  the 
1  See  Donnan,  Zeit.  Elektrochem. ,  1911,  17,  572. 


160  PHYSICAL  CHEMISTRY 

membrane  is  permeable.  In  the  first  case,  the  cation 
of  the  added  salt  and  the  anion  of  the  original  salt 
could  cross  the  membrane  together  in  electrically  equiva- 
lent quantities ;  in  the  second  case,  there  would  be  an 
exchange  of  the  two  anions,  also  in  electrically  equiva- 
lent quantities. 

This  is  not  an  imaginary  picture,  for  investigations 
by  Hamburger,  Koppe,  and  others1  have  shown  that 
the  plasmatic  membrane  of  blood  corpuscles  is  generally 
permeable  to  anions.  Some  of  the  facts  which  support 
this  conclusion  may  be  quoted  briefly.  When  a  current 
of  carbon  dioxide  is  passed  through  blood,  chlorine 
passes  from  the  serum  into  the  corpuscles,  and  the 
alkalinity  of  the  serum  increases.  Again,  if  blood  cor- 
puscles are  separated  by  centrifuging,  suspended  in 
an  isotonic  solution  of  a  neutral  sodium  salt  and  sub- 
jected to  a  current  of  carbon  dioxide,  the  salt  solution 
becomes  strongly  alkaline.  If,  on  the  other  hand,  the 
separated  corpuscles  are  suspended  in  an  isotonic  solu- 
tion of  sucrose  or  dextrose  and  there  subjected  to  a 
current  of  carbon  dioxide,  no  alkalinity  results.  The 
most  satisfactory  explanation  of  these  phenomena  is 
based  on  the  view  that  the  carbon  dioxide  penetrates 
the  covering  of  the  blood  corpuscles,  and  reacting  with 
some  of  the  corpuscle  contents,  probably  the  proteins, 
gives  rise  to  the  carbonate  ions  HC03'  and  C08".  The 
plasmatic  membrane  being  permeable  to  anions,  an  ex- 
change between  these  carbonate  ions  and  chlorine  ions 
in  the  surrounding  fluid  becomes  possible,  and  leads  to 
the  production  of  sodium  carbonate,  and  consequent 
alkalinity,  in  the  sodium  salt  solution. 

Emphasis  has  already  been  laid  on  the  condition 
that  any  such  exchange  of  ions  across  a  membrane 

1  Hamburger,  Zeitsch.  £iol.,  1891,  28,"405 ;  v.  Limbeck,  Arch,  exper. 
Pathol.,1835,  35,  309  ;  Koppe,  Pflilger's  Arch.,  1897,  67,  189;  Hamburger 
#nd  van  Lier,  Engdmanris  Arch.  PhysioL,  1902,  492. 


ELECTROLYTIC  DISSOCIATION  161 

must  take  place  in  electrically  equivalent  proportions. 
If  in  the  case  of  blood  corpuscles  the  C03"  ion  is  ex- 
changing with  the  Cr  ion,  it  is  obvious  that  for  every 
carbonate  ion  that  leaves  a  corpuscle  two  chlorine  ions 
must  enter ;  in  order  to  preserve  osmotic  equilibrium 
between  the  corpuscle  contents  and  the  surrounding 
solution,  water  also  must  pass  in,  and  the  bulk  of 
the  corpuscles  must  increase.  No  such  increase  in 
the  volume  of  the  corpuscles  is  to  be  expected  if  the 
C03"  ion  is  exchanging  with  the  S04"  ion.  The  correct- 
ness of  this  line  of  argument  has  been  confirmed  by 
experiment  in  the  following  way.  Equal  quantities  of 
blood  corpuscles  are  suspended  in  isotonic  solutions  of 
(1)  sucrose,  (2)  sodium  sulphate,  (3)  sodium  chloride, 
(4)  sodium  nitrate,  (5)  potassium  nitrate,  and  a  current 
of  carbon  dioxide  is  passed  in  each  case.  The  volumes 
occupied  by  the  corpuscles  after  ceiitrifuging  are  equal 
for  cases  (1)  and  (2),  equal  also  for  cases  (3),  (4), 
and  (5),  but  greater  for  the  second  set  than  for  the 
first. 

From  recent  investigations  it  appears  that  the  cover- 
ing of  red  blood  corpuscles  is  permeable  not  only  for 
anions,  but  also,  in  certain  cases  at  least,  for  cations. 
According  to  Hamburger,1  when  a  small  quantity  of 
calcium  chloride  is  added  to  bullock's  blood,  the  calcium 
distributes  itself  between  serum  and  corpuscles,  that  is, 
the  covering  of  the  corpuscles  is  permeable  to  the 
calcium  ion.  *  Such  corpuscles,  further,  into  which 
calcium  has  thus  penetrated,  lose  the  extra  amount 
they  have  taken  up  when  they  are  washed  with  normal 
serum ;  the  calcium  ion,  that  is,  can  pass  out  as  well 
as  in.  Hamburger  maintains  that  the  passage  of  calcium 
ions  into  the  corpuscles  occurs  only  when  an  exchange 
with  other  cations  is  possible. 

1  Zeit.  physikal.  Chem.,  1909,  69,  663. 


162  PHYSICAL   CHEMISTRY 

If  it  should  turn  out  on  further  investigation  that  the 
red  blood  corpuscles  are  permeable  for  cations  generally, 
then  Overton's  generalisation,  according  to  which  the 
permeability  relationships  of  plant  and  animal  cell  mem- 
branes are  alike  (see  p.  80),  would  have  to  be  modified. 

Specific  Action  of  Ions. — In  the  foregoing  para- 
graphs attention  has  been  drawn  to  a  property  possessed 
by  only  one  ion  of  an  electrolyte,  the  manifestation  of 
which  is  restricted  by  the  action  of  electrostatic  forces. 
There  are,  however,  other  properties  which  are  specifically 
characteristic  of  either  the  anion  or  the  cation,  and  the 
manifestation  of  which  is  free  from  any  such  limitation. 
That  we  should  be  able  to  detect  the  specific  activity 
of  any  one  ion  is  only  natural  in  view  of  the  generally 
additive  character  of  the  properties  of  electrolytes,  and  is 
further  in  harmony  with  the  comparative  independence  of 
the  ions  postulated  by  the  electrolytic  dissociation  theory. 

The  influence  of  various  alkali  salts  on  the  contractility 
of  muscle  may  be  taken  as  an  instance  of  the  way  in 
which  a  specific  property  is  associated  with  some  parti- 
cular ion  or  ions.  On  p.  138  it  was  stated  that  if  a 
frog  muscle  is  allowed  to  lie  in  isotonic  sucrose  or 
dextrose  solution  long  enough  to  extract  all  the  salts 
from  the  fluid  which  bathes  the  muscle  fibres,  the  muscle 
loses  its  power  of  transmitting  or  responding  to  a 
stimulus.  The  contractility,  however,  is  restored  on 
treatment  of  the  muscle  with  solutions  of  sodium  salts. 
Any  sodium  salt  serves  for  this  purpose ;  the  character 
of  the  anion  with  which  the  sodium  is  associated  is 
practically  immaterial.1  This  observation  in  the  physio- 
logical field  is  closely  related  to  the  fact,  already  dis- 
cussed, that  the  chemical  reactions  of  salt  solutions  are 
additive  in  character;  the  solutions  of  calcium  salts, 

1  Overton,  Pflilgers  Archiv.,  1904,  105,  176. 


ELECTROLYTIC   DISSOCIATION  163 

for  instance,  give  certain  reactions  which  are  the  same 
whether  it  is  the  nitrate,  the  chloride,  or  the  sulphate 
which  is  employed;  the  character  of  the  anion  with 
which  the  calcium  is  associated  is  immaterial.  In  con- 
trast to  the  power  of  sodium  salts  to  restore  the 
contractility  of  muscle  stands  the  behaviour  of  potas- 
sium salts ;  none  of  these  is  able  to  neutralise  the 
paralysing  effect  of  treatment  with  sucrose  solution. 
Further  investigation  on  these  lines  shows  that  the 
sodium  salts  are  in  a  category  by  themselves,  and  that 
the  maintenance  of  contractility  is  a  specific  function 
of  the  sodium  ion. 

In  this  or  any  other  case  where  some  effect  is  specifi- 
cally associated  with  the  one  ion  of  an  electrolyte  as 
distinct  from  the  other  ion  and  from  the  undissociated 
molecule,  then  the  magnitude  of  the  effect  ought  mani- 
festly to  depend  on  the  degree  of  the  ionisation.  This 
conclusion  has  been  verified  to  some  extent  by  the  work 
of  Paul  and  Kronig1  on  the  germicidal  effect  of  various 
salts.  For  the  purpose  of  comparison  the  salt  solutions 
were  allowed  to  act  for  a  given  time  on  approximately 
equal  numbers  of  anthrax  spores,  and  the  number  of 
colonies  which  developed  subsequently  was  taken  as  a 
measure  of  the  germicidal  power  of  the  salt  solution. 
Other  conditions  being  kept  uniform,  it  was  found  that 
the  number  of  colonies  which  develop  after  treatment 
of  the  spores  with  a  given  salt  decreases  as  the  treat- 
ment is  prolonged  and  as  the  concentration  of  the  salt 
solution  is  increased.  For  equally  concentrated  solutions 
of  salts,  all  containing  a  cation  of  marked  germicidal 
power,  the  number  of  colonies  developed  ought  to  in- 
crease as  the  degree  of  dissociation  diminishes.  Paul 
and  Kronig  tested  this  contention  by  comparing  the 
disinfecting  power  of  mercuric  chloride,  bromide,  and 

1  Zdt.  physikal.  Chem.,  1896,  21,  414. 


164  PHYSICAL   CHEMISTRY 

cyanide ;  it  is  known  that  for  equat  concentrations  of 
these  salts  the  degree  of  dissociation  is  greatest  in  the 
case  of  the  chloride,  and  least  in  the  case  of  the  cyanide. 
The  following  table  gives  the  results  obtained : — 

Number  of  Colonies  developed  after 
Disinfecting  Solution.  Treatment  lasting  for 

20  Minutes.  85  Minutes. 

HgCl2        (1  mol.  in  64  litres)  7  0 

HgBr2       (       „  „      „     )  34  0 

Hg(CN)2  (      „          16     „     )  oo  33 

On  the  assumption  that  the  germicidal  effect  of  the 
undissociated  molecules  and  of  the  anions  is  negligible, 
these  figures  are  in  harmony  with  the  view  that  the 
degree  of  dissociation  of  the  three  mercury  salts  increases 
from  the  cyanide  to  the  chloride.  So  far  therefore  we 
may  lay  down  the  proposition  that  the  disinfecting  power 
depends  not  on  the  total  concentration  of  mercury  salt, 
but  on  the  concentration  of  the  mercuric  ion.1  But 
when  mercury  salts  other  than  the  halogen  salts  are 
investigated,  it  appears  that  the  concentration  of  the 
mercuric  ion  is  not  the  only  factor  which  determines 
the  germicidal  power.  Paul  and  Kronig  found  that 
mercuric  nitrate,  although  dissociated  to  a  much  greater 
extent  than  mercuric  chloride,  has  a  much  weaker 
germicidal  effect.  According  to  Hober,  this  is  due  to 
the  fact  that  of  the  two  salts  the  chloride  alone  is 
soluble  in  the  lipoid  substances  of  which  the  living  cell 
membrane  consists;  in  virtue  of  this  it  is  able  to  get 

1  Interesting  evidence  as  to  the  specific  action  of  the  mercuric  ion 
is  supplied  by  Senter's  study  of  the  influence  of  various  substances  on 
the  catalytic  efficiency  of  hsemase  (Zeit.  physikal.  Chem.,  1905,  51,  673). 
It  was  found  that  hydrocyanic  acid  and  mercuric  chloride,  which  are 
partly  dissociated  substances,  paralyse  the  activity  of  hsemase  much 
more  powerfully  than  mercuric  cyanide,  which  is  practically  undis- 
sociated. 


ELECTROLYTIC   DISSOCIATION  165 

at  the  protoplasm  inside  much  more  rapidly  than  the 
nitrate,  and  its  power  of  penetration  more  than  makes 
up  for  its  deficiency  of  mercuric  ions.  Whether  this 
be  so  or  not,  it  is  evident  that  the  specific  character 
of  an  ion,  as  regards  germicidal  action  at  least,  is  liable 
to  be  masked  by  the  intervention  of  other  factors.  This 
is  what  happens  in  the  case  of  acids  regarded  as  dis- 
infecting agents.  Acids  are  alike  in  that  when  dissolved 
in  water  they  all  yield  hydrogen  ions  to  a  greater  or 
less  extent,  and  it  has  been  shown  by  Paul  and  Kronig 
that  the  germicidal  effect  of  an  acid  is  in  the  first 
place  determined  by  its  degree  of  dissociation,  that  in 
fact  the  hydrogen  ion  has  a  specific  toxic  action.1  The 
weaker  acids,  however,  are  more  toxic  than  we  should 
expect  if  there  were  a  complete  parallelism  between 
germicidal  power  and  degree  of  dissociation ;  acetic  acid, 
for  instance,  which  from  the  figures  recorded  on  p.  131, 
is  seen  to  be  feebly  dissociated,  is  in  regard  to  toxic 
power  not  far  behind  hydrochloric  acid,  which  is  highly 
dissociated.  Here,  according  to  Overton,  it  is  the  solu- 
bility of  the  undissociated  molecules  of  the  organic 
acids  in  the  plasmatic  membrane  which  accounts  for 
their  exceptional  toxic  power. 

A  case  where  it  is  pre-eminently  the  undissociated 
molecule  of  an  acid,  and  not  the  hydrogen  ion,  which 
exerts  a  specific  action  is  found  in  connection  with 
artificial  parthenogenesis.2  It  appears  from  Loeb's  inves- 
tigations that  unfertilised  eggs  of  Slrongylocentrotus  pur- 
puratus,  when  placed  for  1|— 2  minutes  in  a  mixture  of 

N 
50  cub.  cm.  sea-water +  3  cub.   cm.   ^  butyric  acid  (or 

other  monobasic  fatty  acid),  and  then  replaced  in  normal 
sea-water,  develop  a  typical  fertilisation  membrane.  The 

1  Compare  Senter,  loc.  cit. 

2  Loeb  ;  see  p.  73. 


166  PHYSICAL  CHEMISTRY 

minimum  concentration  of  monobasic  fatty  acid  necessary 
for  the  production  of  the  membrane  diminishes  as  the 
number  of  carbon  atoms  in  the  molecule  of  the  acid 
increases.  Further,  the  strong  mineral  acids,  hydro- 
chloric, sulphuric,  and  nitric  acids,  are  much  less  effective 
than  the  monobasic  fatty  acids;  it  was  found  that 
so  far  as  inducing  the  formation  of  a  membrane  is  con- 

N  N 

cerned,  butyric  acid   is  more  effective  than  =    HC1. 


All  the  evidence,  in  fact,  goes  to  show  that  it  is  the 
undissociated  acid  molecule  which  penetrates  the  egg 
and  brings  about  the  formation  of  the  membrane. 

Hydrogen  and  Hydroxyl  Ions.  —  The  hydrogen  ion 
has  been  alluded  to  as  possessing  a  specific  toxic  power, 
but  all  the  characteristic  properties  of  acid  solutions  are 
to  be  regarded  as  associated  specially  with  this  ion. 
Similarly  the  hydroxyl  ion,  present  in  the  solutions  of 
bases,  confers  on  these  solutions  certain  well-marked 
properties,  which  are  to  be  regarded  as  characteristic 
of  this  ion. 

The  hydrogen  and  hydroxyl  ions  merit  more  detailed 
consideration,  not  only  because  acids  and  bases  are  such 
important  groups  of  electrolytes,  but  also  because  these 
ions  are  exceptional  in  various  ways.  Reference  to  the 
table  of  ionic  conductivities  shows  that  these  two  ions 
are  far  and  away  more  mobile  than  any  others,  either 
cations  or  anions.  This  fact,  as  the  argument  on  p.  157 
shows,  involves  the  consequence  that  in  regard  to  diffusive 
power  acids  and  bases  surpass  all  salts.  '  Again,  the 
hydrogen  and  hydroxyl  ions  are  those  which  by  their 
combination  yield  a  molecule  of  water,  and  it  has  been 
suggested  that  this  circumstance  has  something  to  do 
with  their  exceptionally  high  ionic  velocities.  The 
hydrogen  ion,  it  is  supposed,  travelling  under  the  in- 


ELECTROLYTIC   DISSOCIATION  167 

fluence  of  an  electric  force  through  an  aqueous  solution 
of  an  acid,  collides  with  the  anion  side  of  a  water 
molecule  and  displaces  the  hydrogen  from  the  other 
side.  This  new  hydrogen  ion  carries  on  the  charge 
until  it  collides  with  a  water  molecule,  when  the  process 
is  repeated.  In  this  way,  it  is  supposed,  the  real  distance 
to  be  traversed  between  the  two  electrodes  is  shortened, 
so  that  the  mobility  of  the  hydrogen  ion  appears  to 
be  greater  than  it  really  is. 1 

In  regard  also  to  their  power  of  acting  as  catalytic, 
agents  the  hydrogen  and  hydroxyl  ions  occupy  an  ex- 
ceptional position.  There  are  numerous  reactions,  for 
instance,  which  take  place  with  appreciable  rapidity 
only  in  the  presence  of  acids,  and  it  is  found  that  the 
rate  of  the  reaction  is  approximately  proportional  to 
the  concentration  of  the  hydrogen  ions.  The  inversion 
of  sucrose  is  a  case  in  point,  and  the  parallelism  between 
the  velocity  of  this  change  under  the  influence  of  various 
acids  and  the  concentration  of  the  hydrogen  ions  in 
each  case  is  clearly  shown  by  the  following  table.2  The 
figures  refer  to  equivalent  quantities  of  the  various  acids, 
and  hydrochloric  acid  is  taken  as  the  standard  in  con- 
nection both  with  the  velocity  and  the  hydrogen  ion 
concentration.  The  actual  method  of  measuring  the 
velocity  of  inversion  will  be  discussed  later,  but  for  the 
present  the  figures  in  Column  I.  may  be  accepted  as 
representing  the  relative  velocities  of  inversion  under 
the  influence  of  equivalent  quantities  of  different  acids. 
Instead  of  the  hydrogen  ion  concentrations  there  are 
recorded  in  Column  II.  the  relative  conductivities  of 
the  acids  in  equivalent  concentration.  A  strict  measure 
of  the  hydrogen  ion  concentration  would  be  given  by 

1  Tijmstra,  Zeit.  physikcd.  Chem.,  1904, 49,  345  ;  Danneel,  Zeit.  fur  Elek- 
trochcm.,  1905,  11,  249;  Dempwolff,  Physikal.  Zeit.,  1904,  5,  637. 

2  Ostwald,  Journ.  prakt.  Chemie,  1884,  30,  95. 


168  PHYSICAL  CHEMISTRY 

a,   the  degree  of  dissociation  in  each   case,  but  a  =  —  , 

oo 

and  as  the  value  of  X^  does  not  vary  very  much  from 
one  acid  to  another,  the  conductivity  of  each  solution 
may  be  taken  as  an  approximate  measure  of  the  hydrogen 
ion  concentration. 

i.  n. 

HC1 100  100 

CHC19.COOH     ....       27  25 
CH2C1.COOH     ....         4-8  4-9 

H.COOH 1-5  1-7 

CHg.COOH 0-40  0-42 

The  parallelism  between  the  two  sets  of  figures  is 
unmistakable. 

There  are  other  reactions,  such  as  the  hydrolysis  of 
esters,  which  are  accelerated  by  acids,  and  the  velocity 
of  which  is  approximately  proportional  to  the  concen- 
tration of  the  hydrogen  ion.  The  acceleration  of  these 
reactions  appears  therefore  to  be  a  specific  property 
of  the  hydrogen  ion,  not  of  acids  as  such.  If  this  view 
is  accepted,  then  a  sucrose  solution,  or  a  solution  of 
methyl  acetate,  may  be  regarded  as  a  reagent  for 
hydrogen  ions.  The  presence  of  these  ions  in  any  fluid 
may  be  detected  and  their  amount  estimated  by  studying 
the  influence  of  this  fluid  on  the  inversion  of  sucrose  or 
the  hydrolysis  of  methyl  acetate.  The  information  given 
by  such  an  investigation  is  quite  different  from  that 
given  by  a  titration  of  the  fluid  with  a  standard 
alkali  solution ;  by  this  latter  operation  we  ascertain 
merely  the  total  acid  present,  both  in  the  dissociated 
and  undissociated  conditions. 

Various  reactions  are  similarly  available  for  the  de- 
tection and  estimation  of  the  hydroxyl  ion.  It  is  well 
known  that  esters  are  readily  saponified  or  hydrolysed 
by  alkalis,  and  closer  investigation  of  the  problem  has 
hown  that  the  rate  of  saponification  depends,  not  on 


ELECTROLYTIC   DISSOCIATION  169 

the  total  alkali  concentration,  but  on  that  of  the  hydroxyl 
ions.  The  equation  for  the  hydrolysis  of  ethyl  acetate 
by  sodium  hydroxide  in  dilute  aqueous  solution  is 
generally  written 

CH3.COOC2H5  +  NaOH  =  CH3.COONa  +  C2H5OH, 

but  since  sodium  hydroxide  and  sodium  acetate  are  both 
dissociated  to  a  large  extent  under  these  conditions, 
the  change  would,  from  the  point  of  view  of  the  elec- 
trolytic dissociation  theory,  be  more  correctly  repre- 
sented by 

CH3.COOC2H6  f  Na-  +  OH'  =  CH8.COO'  +  Nrf  +  C2H5OH. 

Since  Na"  occurs  on  both  sides  of  the  equation,  it  may 
be  simplified  to 

CH3.COOC2H5  +  OH'  =  CH3.COO'  4-  C2H5OH. 

In  harmony  with  this  form  of  the  equation  it  is  found, 
as  already  stated,  that  the  velocity  of  saponification  of 
ethyl  acetate  or  other  ester  by  a  base  depends  on  the 
concentration  of  the  hydroxyl  ion  in  the  solution,  and 
is  practically  independent  of  the  positive  radical  of  the 
base.  By  way  of  illustration  the  following  figures  may 
be  quoted.  The  velocity  of  saponification  of  ethyl  acetate 

by  JQ  KOH  at  24f7°  is  represented  by  the  number 
6  '41;  the  corresponding  figure  for  -^  NH4OH  at  the 
same  temperature  is  found  to  be  0*16.  Since  the  degrees 
of  dissociation  for  5  KOH  and  ^  NH4OH  are  respec- 
tively 0-97  and  0-027,  then  on  the  assumption  of  an  exact 
proportionality  between  velocity  of  saponification  and 
hydroxyl  ion  concentration  we  should  expect  for  the 

velocity    of    saponification    by  NH4OH,    the    value 


170  PHYSICAL   CHEMISTRY 

— 0^ =  0'18.     This  figure  is  in  good  agreement  with 

the  value  actually  observed. 

A  reaction  of  a  different  kind  which  is  accelerated  by 
hydroxyl  ions  is  the  change  of  diacetonalcohol  into 
acetone.1  The  velocity  of  this  change  is  found  to  be 
proportional  to  the  concentration  of  the  hydroxyl  ions, 
which  act  purely  as  catalytic  agents,  like  hydrogen  ions 
in  the  inversion  of  sucrose.  The  change  diacetonalcohol 
-» acetone  furnishes,,  therefore,  a  means  of  detecting  the 
presence  and  measuring  the  concentration  of  hydroxyl 
ions  as  distinct  from  undissociated  bases.  It  should  be 
noted,  however,  that  in  the  case  of  weak  bases,  such  as 
ammonia,  there  is  not  by  any  means  exact  proportionality 
between  the  velocity  of  change  and  the  concentration 
of  the  hydroxyl  ions. 

The  Dissociation  of  Water. — Reference  has  already 
been  made  to  the  interest  which  attaches  to  the  hydrogen 
and  hydroxyl  ions  011  the  ground  that  by  their  combina- 
tion they  yield  water.  So  far,  in  fact,  as  aqueous  solutions 
are  concerned,  these  ions  stand  in  a  special  relationship 
to  the  solvent.  The  question  thus  arises :  Does  water 
itself  contain  hydrogen  and  hydroxyl  ions,  and  if  so,  what 
is  the  extent  of  the  dissociation?  It  is  evident  that  in 
any  case  the  proportion  of  hydrogen  and  hydroxyl  ions 
in  water  must  be  comparatively  small,  for,  according  to  the 
view  already  adopted,  an  electric  current  is  able  to  pass 
through  an  aqueous  solution  only  in  so  far  as  there  are 
ions  present.  Pure  water  is  a  very  poor  conductor.  We 
may  compare,  for  instance,  the  specific  conductivity  of 
good  distilled  water,  which  is  about  7xlO~6  at  18°, 
with  that  of  normal  sodium  chloride  solution,  which  is 
7'44xlO~2  at  the  same  temperature.  In  other  terms, 
distilled  water  enclosed  in  a  centimetre  cube,  two  opposite 

1  Koelicben,  Zeit.  physikal.  Ghent.,  1900,  33,  129. 


ELECTROLYTIC   DISSOCIATION  171 

faces  of  which  act  as  electrodes,  offers  a  resistance  of 
about  140,000  ohms,  while  normal  sodium  chloride  solu- 
tion, under  the  same  conditions,  offers  a  resistance  of 
13*4  ohms.  The  conductivity  of  ordinary  distilled  water, 
moreover,  arises  chiefly  from  the  impurities  which  it  con- 
tains, notably  carbon  dioxide,  and  may  be  considerably 
reduced  by  simple  methods.  Kohlrausch  has  shown  that 
when  a  current  of  air  carefully  freed  from  carbon  dioxide 
is  aspirated  for  some  time  through  a  sample  of  dis- 
tilled water  the  conductivity  of  the  latter  is  materially 
diminished,  a  result  due  to  the  removal  of  the  greater 
part  of  the  carbon  dioxide.  This  gas  may  be  got  rid 
of  also  by  redistilling  the  water  and  rejecting  the  first 
portion  of  the  distillate,  in  which  naturally  the  more 
volatile  impurities  of  the  water  are  concentrated.  In 
such  an  operation  great  care  must  be  taken  that  the 
mechanical  carrying  over  of  solid  or  liquid  particles  from 
the  boiler  is  avoided  by  the  introduction  of  a  trap,  and 
that  the  condensed  water  is  brought  into  contact  only 
with  tin  or  the  best  kind  of  glass.  An  apparatus  which 
claims  to  fulfil  these  conditions  has  been  described  by 
Hartley,  Campbell,  and  Poole,1  and  it  is  instructive  to 
note  the  values  which  they  record  for  the  conductivity  of 
the  distillates  obtained  at  various  stages  of  the  distillation. 
The  boiler  used  was  capable  of  holding  about  10  litres,  and 
it  was  found  that  a  considerable  portion  of  this  had  to 
be  distilled  off  before  a  fraction  of  very  low  conductivity 
was  obtained.  This  is  shown  by  the  following  figures : — 

Time  from  Start  Quantity  of  Specific  Conductivity 

of  Boiling.  Fraction  Collected.  of  Fraction. 

Hours.  Litres.  KX108. 

0-5  0-5  >2 

2-5  2-0  1-7 

5-5                            2-75  0-73 

6-5                             1-0  1-0 

1  Journ.  Chcm.  Soc  ,  1908,  93,  428.     Compare  Bourdillon,  ibid.,  1913, 
103,  791. 


172  PHYSICAL  CHEMISTRY 

The  middle  portion  of  the  distillate  is  the  purest,  and 
is  that  which  should  be  employed  in  the  preparation  of 
solutions  for  conductivity  work  (see  p.  126).  Nothing- 
is  to  be  gained  by  producing  still  purer  water  for  ordinary 
investigations  of  conductivity,  because  even  a  sample  for 
which  KX  106  =  0*75  —  TO  deteriorates  during  the  contact 
with  air  which  unavoidably  occurs  in  the  transference 
from  the  storage  flask  to  the  conductivity  cell. 

It  is,  however,  an  interesting  question  how  far  water 
can  be  freed  from  adventitious  electrolytic  impurities, 
and  whether  the  residual  conductivity  then  obtained  is 
to  be  attributed  to  the  dissociation  of  the  water  itself. 
Kohlrausch  has  pushed  the  purification  of  water  to  its 
utmost  limit,  and  by  distillation  of  a  specially  purified 
sample  in  vacuo  has  obtained  water  for  which  K  x  106=  0*04 
at  18°.  If  this  figure  is  taken  as  representing  the  con- 
ductivity of  absolutely  pure  water,  then  it  is  possible  to 
calculate  the  concentration  of  the  hydrogen  and  hydroxyl 
ions  in  this  liquid.  For  this  purpose  we  may  regard 
pure  water  as  a  very  dilute  solution  containing  hydrogen 
and  hydroxyl  ions,  and  the  equivalent  conductivity  must, 
according  to  Kohlrausch's  law,  be  very  nearly  equal  to 
nn  '  ^OH  =  318  +  174  =  492,  for  the  ionic  conductivities 
of  the  two  ions  at  18°  are  respectively  318  and  174. 
Now  KX<!>  =  \,  where  <£>  is  the  volume  in  cub.  cm. 
which  contains  1  gram  -  equivalent  of  each  ion,  and 

(ft  =  ^=       49^       =12-3xl09   cub.   cm.  =  12-3xl06  litres. 

K       U  U4  X  ID 

That  is  to  say,  the  quantity  of  water  which  contains 
1  gram  of  hydrogen  in  the  ionic  form  is  over  12  million 
litres.  The  significance  of  this  figure  is  open  to  criticism, 
in  so  far  as  Kohlrausch's  investigations  furnish  of  them- 
selves no  definite  proof  that  the  figure  0'04xlO~6  is  the 
conductivity  of  absolutely  pure  water.  By  three  other 
independent  methods,  however,  a  vaiue  has  been  deduced 


ELECTROLYTIC   DISSOCIATION  173 

for  the  dissociation  of  water  which  is  in  good  agreement 
with  that  calculated  from  the  conductivity.  There  are 
therefore  reasonable  grounds  for  the  view  that  the  residual 
conductivity  observed  by  Kohlrausch  for  his  purest  water 
is  to  be  attributed  to  the  dissociation  of  the  water  itself, 
and  not  to  any  impurities  which  it  still  contained. 

Complex  Ions. — In  the  earlier  part  of  this  chapter 
reference  has  been  made  to  the  additive  character  of  the 
reactions  of  salt  solutions — the  fact  on  which  the  practice 
of  the  analytical  chemist  is  based :  the  wet  reactions 
so  frequently  employed  are  tests  for  the  presence  of 
various  ions,  not  for  salts  as  a  whole.  In  this  connection 
it  is  noteworthy  that  a  metal  which  enters  into  the  com- 
position of  a  dissolved  salt,  although  it  generally  forms 
the  cation  of  the  solution,  does  not  do  so  invariably. 
Frequently  it  becomes  part  of  a  complex  aiiion,  and  as 
each  ion  has  its  characteristic  reactions,  the  tests  which 
are  employed  to  recognise  the  metal  in  the  cationic  con- 
dition gave  no  result  in  this  case.  A  simple  illustration 
is  furnished  by  silver  in  potassium  cyanide  solution.  If 
potassium  cyanide  is  added  to  a  solution  of  silver  nitrate 
a  precipitate  of  silver  cyanide  is  obtained,  which,  however, 
dissolves  up  again  when  excess  of  potassium  cyanide  is 
added.  The  solution  so  prepared  does  not  answer  to  the 
ordinary  test  for  silver:  sodium  chloride  may  be  added 
without  producing  any  precipitate.  The  natural  con- 
clusion is  that  there  can  be  no  appreciable  quantity  of 
silver  ions  in  the  solution,  and  the  question  then  arises : 
In  what  form  is  the  silver  present?  The  answer  to 
this  question  was  furnished  long  ago  by  Hittorf,  who 
showed  that  when  a  solution  of  silver  cyanide  in  potassium 
cyanide  is  electrolysed  the  silver  migrates  from  the  cathode 
to  the  anode,  while  of  course  in  the  case  of  an  ordinary 
silver  salt  solution  the  silver  travels  as  cation  from  anode 


174 


PHYSICAL   CHEMISTRY 


to  cathode.  In  the  cyanide  solution,  therefore,  the  silver 
must  be  part  of  the  anion,  and  when  the  changes  of  con- 
centration occurring  at  the  electrodes  during  electrolysis  are 
determined,  it  appears,  as  Hittorf  showed,  that  the  ions  are 

K  and  Ag(CN)2. 

The  transport  of  a  metal  from  cathode  to  anode  as 
part  of  a  complex  anion  may  be  demonstrated  directly 
in  those  cases  where  the  anion  in  question  possesses  a 
characteristic  colour.  It  is  possible,  for  instance,  to  detect 
easily  by  an  electrolytic  experiment  the  difference  be- 
tween copper  in  a  solution  of  copper  sulphate  and  copper 
in  Fehling's  solution.1  Two  thistle  funnels  are  sealed 
together  so  that  the  total  length  of  the  tube  between  the 
bulbs  is  about  30  cm.  The  tube  is  then  bent  as  shown 
in  Fig.  21.  A  normal  solution  of  sodium  chloride  in  12 


FIG.  21. 

per  cent,  gelatin  is  run  into  the  tube  from  B  to  D  and 
allowed  to  set.  One  of  the  bulbs,  A,  is  then  filled  with 
copper  sulphate  solution,  the  other,  C,  is  charged  with 
the  deep  blue  neutral  solution  which  is  obtained  when 
cupric  tartrate  is  dissolved  in  caustic  potash,  excess 
of  the  alkali  being  avoided.  Platinum  electrodes  are 
immersed  in  these  two  solutions,  and  are  so  connected 
with  a  source  of  current,  that  the  electrode  which  dips  in 
1  See  Masson,  Journ.  Chem.  Soc.,  1899,  75,  725. 


ELECTROLYTIC   DISSOCIATION  175 

the  copper  sulphate  solution  acts  as  anode.  The  E.M.F. 
applied  to  the  electrodes  ought  to  be  about  30  volts,  and 
the  tube  containing  the  jelly  is  kept  in  cold  water  during 
the  experiment.  After  the  current  has  passed  for  some 
time  it  is  observed  that  the  end  of  the  jelly  column 
next  A  is  coloured  pale  blue;  that  is,  the  copper  ions 
are  migrating  from  anode  to  cathode.  The  other  end  of 
the  jelly  column,  however,  is  also  coloured  blue,  of  a 
deeper  shade,  showing  that  complex  ions  containing  copper 
are  moving  from  cathode  to  anode. 

A  similar  method  has  been  employed  by  Donnan  and 
Bassett 1  to  show  that  the  blue  colour  exhibited  by  cobalt 
chloride  solutions  under  certain  conditions  is  to  be 
attributed  to  the  presence  of  a  complex  anion  contain- 
ing cobalt. 

Evidence  of  the  formation  of  a  complex  salt  is  fre- 
quently found  in  an  increase  of  solubility.  As  a  general 
rule,  the  solubility  of  a  salt  is  diminished  in  presence 
of  another  salt  with  a  common  ion ;  thus,  for  example, 
sodium  chloride  is  less  soluble  in  hydrochloric  acid 
than  in  pure  water  at  the  same  temperature.  There 
are,  however,  numerous  cases  where  an  increase  of  solu- 
bility occurs  on  adding  a  salt  with  a  common  ion ;  thus 
silver  cyanide  is  soluble  in  potassium  cyanide,  and  mer- 
curic chloride  is  more  soluble  in  sodium  chloride  solution 
than  in  pure  water.  In  both  these  cases  complex  salts 
are  formed,  and  the  metal  becomes  part  of  the  anion, 
so  that  the  concentrations  of  Ag"  and  Hg",  even  if  not 
quite  nil,  are  exceedingly  small. 

In  view  of  this,  it  is  only  natural  that,  as  shown  by 
Paul  and  Kroiiig,2  the  germicidal  power  of  a  solution 
containing  1  mol.  AgN03  +  2  mols.  KCN  in  4  litres  is 
exceedingly  small  compared  with  that  of  a  solution  con- 

1  Journ.  Chcm.  Soc.,  1902,  81,  939. 

2  Zeit.  physical.  Chem.,  1896,  21,  425. 

M 


176  PHYSICAL  CHEMISTRY 

taiiiing  1  mol.  AgN03  in  4  litres.  The  silver  ion,  which 
is  responsible  for  the  toxic  effect,  is  present  in  the  first 
solution  only  to  a  very  small  extent.  Similarly,  the 
germicidal  power  of  mercuric  chloride  is  much  reduced 
when  sodium  chloride  is  present  in  the  solution ;  the 
addition  of  the  latter  salt  involves  the  disappearance 
of  mercuric  ion  as  such,  and  its  conversion  into  a  com- 
plex anion  of  weak  toxic  power. 

Another  case  of  the  formation  of  complex  ions  may 
be  mentioned.  It  is  well  known  that  a  solution  of 
copper  sulphate  to  which  sucrose  has  been  added  fails 
to  answer  to  the  ordinary  tests  for  copper  ;  potassium 
hydroxide  may  be  added  to  the  solution  without  causing 
any  precipitate.  In  harmony  with  this  it  has  been  found 
by  Kahlenberg,1  that  in  a  solution  containing  sucrose, 
copper  sulphate,  and  potassium  hydroxide  in  the  pro- 
portions represented  by  C12H22On  +  CuS04  f  3KOH  there 
are  practically  no  copper  ions.  Further,  Kahlenberg  and 
True  have  shown2  that  while  seedlings  of  Lupinus 
albus  L.  are  killed  in  a  solution  containing  a  very 
minute  quantity  of  copper  ion,  they  are  able  to  grow 
in  a  solution  containing  sucrose,  copper  sulphate,  and 
potassium  hydroxide  in  the  afore-meiitioiied  proportions, 
even  when  the  amount  of  copper  present  is  as  much  as 
TJ^fth  of  a  gram-atom  per  litre.  It  makes,  in  fact,  a 
great  deal  of  difference  whether  the  copper  is  present 
as  Cu"  or  as  part  of  a  complex  ion. 

1  Zeit.  physikal.  Chem.y  1895,  17,  612. 

2  Bot.  Gazette,  1896,  22,  81. 


CHAPTEE   IX 

COLLOIDAL   SOLUTIONS 

Crystalloids  and  Colloids. — In  the  preceding  chapters 
dealing  with  the  physical  and  biological  characteristics 
of  aqueous  solutions  reference  has  been  made  almost 
exclusively  to  solutions  of  such  substances  as  sugar, 
salt,  glycerine,  acetic  acid,  and  potassium  nitrate.  These 
compounds  have  been  classed  as  electrolytes  or  non- 
electrolytes,  according  to  the  osmotic  activity  of  their 
solutions,  and  their  power  to  conduct  the  electric  current. 
There  is,  however,  a  large  class  of  substances  which,  on 
account  of  their  special  characteristics,  must  be  distin- 
guished both  from  electrolytes  and  non- electrolytes,  as 
these  terms  are  ordinarily  understood.  It  was  Graham 
who  first  made  this  distinction,  and  pointed  out  that 
substances  which  crystallised  readily  from  water  were 
characterised  by  high  diffusive  power,  and  by  the  ability 
to  pass  through  animal  or  vegetable  membranes ;  those 
substances,  on  the  other  hand,  which  cannot  easily  be 
obtained  in  the  crystallised  condition,  amorphous  sub- 
stances in  fact,  are  characterised  by  low  diffusive  power 
and  by  inability  to  pass  through  animal  and  vegetable 
membranes.  The  substances  belonging  to  the  first  class, 
such  as  sucrose  or  sodium  chloride,  Graham  termed 
crystalloids ;  those  belonging  to  the  second  class,  such 
as  starch,  gum,  albumin,  and  caramel,  he  termed 
colloids.  Solutions  of  these  latter  substances  differ  in 
many  respects  from  those  of  crystalloids ;  they  are  of 
great  interest  and  importance  on  both  physical  and 

177 


178  PHYSICAL  CHEMISTRY 

biological  grounds,  and  they  merit  special  consideration 
from  the  point  of  view  adopted  in  this  volume. 

At  the  outset  it  ought  to  be  explained  that  the 
term  '  colloid '  is  now  employed  in  a  sense  somewhat 
different  from  that  in  which  Graham  used  it.  It  is 
generally  interpreted  at  the  present  time  as  referring, 
not  so  much  to  a  certain  class  of  substances,  but  rather 
to  a  condition  which  a  large  number  of  chemical  com- 
pounds may  assume  more  or  less  readily.1  A  *  colloidal 
solution/  therefore,  is  not  necessarily  a  solution  of  a 
colloid  (in  Graham's  sense);  it  is  to  be  interpreted  as 
a  solution  the  special  characteristics  of  which  are  similar 
to  those,  say,  of  a  gum,  but  the  dissolved  substance 
may  be  quite  outside  the  class  which  Graham  termed 
'  colloids ' ;  it  may  be,  for  instance,  ferric  hydroxide, 
arsenious  sulphide,  or  platinum.  These  latter  sub- 
stances, it  is  true,  differ  from  guru,  albumin,  &c.,  in 
that  they  can  be  persuaded  to  form  a  colloidal  solution 
only  in  an  indirect  way ;  mere  contact  with  water, 
however  prolonged,  will  not  bring  ferric  hydroxide  or 
arsenious  sulphide  into  solution.  The  precipitation 
of  these  substances,  therefore,  from  their  colloidal  solu- 
tions cannot  be  directly  reversed,  and  they  are  accord- 
ingly sometimes  termed  '  irreversible '  colloids,  in 
contrast  to  gum,  albumin,  &c.,  which  belong  to  the 
class  of  *  reversible '  colloids,  and  are  directly  soluble 
in  water.  There  are  other  points  of  contrast  between  a 
reversible  and  an  irreversible  colloid,  which  will  appear 
later. 

The  substance  which  forms  a  colloidal  solution  is,  as 
Graham  showed,  characterised  by  inability  to  pass  through 
an  animal  or  vegetable  membrane,  and  on  this  fact  is 
based  the  use  of  dialysis  as  a  means  of  preparing  a 
colloidal  solution,  free  from  dissolved  crystalloids.  A 

1  See  Ostwald,  Grundriss  der  cdlgemeinen  Chemie  (1909).  p.  548. 


COLLOIDAL   SOLUTIONS  179 

piece  of  parchment  or  bladder  is  tied  over  one  end  of  a 
wide  glass  cylinder,  and  into  the  receptacle  so  formed, 
a  '  dialyser,'  as  it  is  called,  the  solution  which  is  to  be 
purified  from  crystalloids  is  poured.  The  lower  end  of 
the  dialyser  is  then  immersed  in  water,  into  which  the 
crystalloids  gradually  diffuse  through  the  membrane 
closing  the  dialyser.  If  the  water  is  frequently  re- 
newed the  colloidal  solution  inside  is  soon  practically 
free  from  salts  or  other  crystalloids,  although  it  is  very 
difficult  to  remove  the  last  traces  of  these  substances. 
Instead  of  a  dialyser  of  the  kind  just  described,  a  simple 
tube  made  of  parchment  paper  may  be  employed. 
Charged  with  the  colloidal  solution,  it  is  hung  up  by 
its  ends  and  suspended  in  a  vessel  through  which  pure 
water  is  kept  flowing.  As  an  example  of  the  use  of 
dialysis,  the  preparation  of  a  solution  of  silicic  acid 
may  be  taken.  When  a  solution  of  sodium  silicate  is 
poured  into  excess  of  hydrochloric  acid,  the  silicic  acid 
which  is  formed  remains  in  solution  along  with  sodium 
chloride  and  the  extra  hydrochloric  acid  :  the  mixture 
is  subjected  to  dialysis,  in  the  course  of  which  the  sodium 
chloride  and  hydrochloric  acid  diffuse  out  through  the 
membrane  of  the  dialyser,  leaving  behind  a  colloidal  solu- 
tion of  silicic  acid.  Dialysis  may  be  similarly  employed 
in  preparing  a  colloidal  solution  of  ferric  hydroxide,  or 
in  freeing  a  solution  of  egg  albumin  from  admixed  salts. 

As  Graham  pointed  out,  there  is  a  marked  difference 
in  the  diffusive  power  of  crystalloids  and  colloids.  This 
appears  from  the  following  figures,  which  represent  the 
relative  times  required  for  equal  diffusion  of  two  crystal- 
loids and  two  colloids,  sodium  chloride*"  being  taken  as 
the  standard  of  comparison :  sodium  chloride,"  1 ;  sucrose, 
3  ;  egg  albumin,  21 ;  caramel,  42.  The  diffusion  of  enzymes 
has  recently  l  been  investigated,  and  it  appears  that  these 
1  Herzog,  Zeit.  Electrochem.,  1907,  13,  533. 


180  PHYSICAL  CHEMISTEY 

substances,  like  others  which  form  colloidal  solutions,  are 
characterised  by  low  diffusive  power. 

Osmotic    Pressure    of    Colloidal    Solutions.— In  an 

earlier  chapter  it  has  been  suggested  that  the  phenomenon 
of  diffusion  in  solution  is  closely  connected  with  osmotic 
pressure.  If  there  is  such  a  connection,  it  is  to  be 
expected  that  the  solution  of  a  colloid,  characterised  as 
it  is  by  a  low  rate  of  diffusion,  will  exert  at  the  most 
only  a  small  osmotic  pressure.  This  conclusion  is  con- 
firmed by  experimental  work,  as  will  appear  from  the 
examples  quoted  below.  In  some  cases  indeed  colloidal 
solutions  have  been  found  to  exhibit  no  osmotic  activity 
whatsoever ;  Reid,1  for  instance,  working  with  carefully 
purified  albumin  solutions,  came  to  the  conclusion  that 
these  exert  no  osmotic  pressure.  In  any  investigation  of 
the  osmotic  activity  of  a  colloid,  the  question  whether 
the  solution  is  absolutely  free  from  electrolytes  is  of 
the  utmost  importance ;  an  electrolyte  is  highly  active 
material  from  the  osmotic  point  of  view,  and  a  small  trace 
present  in  a  colloidal  solution  may  easily  lead  to  erroneous 
conclusions.  As  has  been  hinted  already,  it  is  not  easy  to 
remove  the  last  traces  of  electrolytes  from  a  colloidal 
solution,  and  there  can  be  no  doubt  that  the  older 
determinations  of  the  osmotic  pressure  of  colloids,  such 
as  those  made  by  Pfeffer  on  gum  arabic,  gave  too 
high  values,  owing  to  the  presence  of  electrolytic 
material.  Recent  investigators  who  have  determined 
the  osmotic  pressure  of  colloidal  solutions  have  devoted 
much  more  attention  to  the  problem  of  purification,  and 
the  values  given  by  them  may  be  regarded  as  repre- 
senting more  closely  the  real  osmotic  pressure  of  the 
colloid. 

The  osmotic  pressures  of  colloidal   solutions  of  ferric 

1  Journ.  PhysioL,  1904,  31,  438. 


COLLOIDAL   SOLUTIONS  181 

hydroxide  have  been  determined  by  Duclaux,1  and  the 
values  obtained  are  recorded  in  the  following  table.  A 

Per  Cent.  Pressure  in 

Fe2(OH)6.  cm.  Water. 

1'08  0'8 

2-04  2'8 

3-05  5 '6 

5-35  12*5 

8-86  22-6 

glance  at  the  figures  will  show  how  small  the  pressures 
are  even  for  the  5 -3 5  per  cent,  and  the  8 '8 6  per  cent, 
solutions:  the  pressure  developed  in  the  latter  case  is 
that  which  would  be  given  by  a  solution  containing 
about  one-thirtieth  of  a  gram  of  sucrose  in  100  grams 
of  water.  The  figures  recorded  in  the  table  show  that 
although  the  osmotic  pressure  increases  with  the  con- 
centration, there  is  not  anything  like  proportionality 
between  the  two  variables. 

More  attention  has  been  devoted  to  the  question  of 
the  osmotic  activity  of  the  serum  proteins,  egg  albumin, 
and  gelatin.  In  his  experiments  on  the  osmotic  pres- 
sure exerted  by  serum  proteins,  Starling2  employed  an 
osmometer,  the  semi-permeable  diaphragm  of  which  con- 
sisted of  peritoneal  membrane  soaked  in  gelatin  and 
supported  by  silver  wire  gauze.  The  osmometer  was 
charged  with  a  solution  of  the  serum  proteins,  the 
other  side  of  the  membrane  being  bathed  by  a  salt 
solution  which  was  approximately  isotonic  with  the 
colloid  solution  in  the  osmometer.  As  the  gelatin 
membrane  was  freely  permeable  to  salts,  the  pressure 
observed  in  the  osmometer  was  attributed  to  the  colloids ; 
the  conclusion  reached  was  that  the  osmotic  pressure  of 
blood  serum  containing  7-8  per  cent,  of  proteins  amounts 
to  25-30  mm.  of  mercury. 

1  Compt.  rend.,  1905,  140,  1544. 

2  Journ.  PhysioL,  1895,  19,  312  ;  1899,  24,  317, 


182  PHYSICAL  CHEMISTRY 

Reid,1  using  a  similar  osmometer  with  a  formalised 
gelatin  membrane,  found  that  when  precipitates  or 
crystals  of  protein  are  repeatedly  washed  with  salt 
solutions,  and  the  osmotic  activity  of  samples  of  the 
material  is  investigated  at  intervals,  the  pressure  observed 
for  1  per  cent,  protein  concentration  falls  off  steadily 
with  continued  washing ;  ultimately,  as  already  indicated, 
solutions  of  protein  are  obtained  which  give  no  osmotic 
pressure.  Haemoglobin,  however,  was  found  to  give  a 
fairly  definite  pressure,  amounting  to  3*51-4*35  mm.  of 
mercury  for  1  per  cent,  concentration  of  haemoglobin.  The 
former  observations  would  seem  to  indicate  that  the  osmotic 
pressure  frequently  found  for  protein  solutions  is  due, 
not  to  the  proteins  themselves  but  to  something  associated 
with  them  which  may  be  gradually  removed.  It  is, 
however,  noteworthy,  on  the  other  hand,  that  the  osmotic 
pressure  developed  by  a  colloidal  solution  is  in  many 
cases  remarkably  steady ;  this  is  difficult  to  explain  if 
the  pressure  is  attributed  to  crystalloids  associated  with 
the  colloid,  for  the  membranes  employed  in  studying 
the  osmotic  activity  of  colloids  are  all  readily  permeable 
to  crystalloids,  so  that  these  could  produce  at  the  most 
only  a  temporary  effect. 

As  an  example  of  the  •  persistence  of  the  osmotic 
pressure  developed  by  a  colloid,  an  observation  made 
by  Moore  and  Roaf 2  may  be  quoted.  These  investi- 
gators have  studied  in  detail  the  behaviour  of  gelatin 
solutions  in  an  osmometer  closed  with  a  parchment 
membrane.  This  osmometer  consisted  of  two  platinum 
capsules  supported  and  held  in  opposition  by  brass 
chambers.  The  rim  of  each  capsule  was  provided  with 
a  flange,  and  between  the  flanges  there  came,  when  the 
apparatus  was  put  together,  a  thick  platinum  grid, 

1  Lnc.  cit. 

2  Biochcm.  Jonrn.    1906,  2,  34. 


COLLOIDAL   SOLUTIONS 


183 


supporting  the  membrane  of  parchment  paper.  Fig.  22 
shows  the  osmometer  fitted  up  and  joined  to  the  manometer. 
In  one  experiment  the  osmometer  was  charged  with 
10  per  cent,  gelatin,  and  a  week  later  the  osmotic  pres- 


FIG.  22. 

sure  was  found  to  be  74  mm.  of  mercury  at  31°  C. ; 
the  experiment  was  continued  for  two  months,  during 
which  time  the  outside  of  the  parchment  membrane 


184  PHYSICAL   CHEMISTRY 

% 

was  constantly  bathed  with  water.  At  the  end  of  that 
period  the  osmotic  pressure  was  found  to  be  70  mm. 
of  mercury  at  26°  C.  Such  a  persistence  of  the  pres- 
sure seems  to  show  that  it  corresponds  to  a  real  equili- 
brium, and  is  not  merely  a  passing  phenomenon  due  to 
slowly  diffusing  crystalloids. 

Other  interesting  observations  made  by  Moore  and 
Eoaf  relate  to  the  influence  of  temperature  on  the 
osmotic  pressure  of  a  gelatin  solution.  The  osmotic 
pressure  increases  with  rising  temperature,  but  the 
increase  is  more  rapid  than  it  would  be  if  the  osmotic 
pressure  were  strictly  proportional  to  the  absolute  tempera- 
ture. Further,  if  a  gelatin  solution,  after  being  kept  for 
a  short  time  at  70-80°,  is  cooled,  say,  to  25°,  the  value 
then  observed  for  the  osmotic  pressure  is  considerably 
higher  than  it  was  before  the  solution  was  heated. 
Only  after  the  solution  has  been,  kept  for  some  days 
at  the  lower  temperature  is  there  a  return  to  the 
former  value.  The  osmotic  pressure  exhibited  by  a 
gelatin  solution  is  therefore  to  some  extent  dependent 
on  its  previous  history.  These  observations  seem  to  be 
most  satisfactorily  interpreted  by  supposing  that  the 
gelatin  solution  contains  large  molecular  groups  or 
aggregates,  which  tend  to  break  up  as  the  temperature 
rises,  thus  leading  to  an  abnormally  great  increase  of 
the  osmotic  pressure.  When  the  solution  is  cooled 
the  large  molecular  aggregates  corresponding  to  the 
lower  temperature  are,  it  may  be  supposed,  re-formed 
only  slowly,  and  until  this  is  complete  the  osmotic 
pressure  is  higher  than  the  true  equilibrium  value. 

This  phenomenon  of  *  hysteresis '  in  connection  with 
the  osmotic  activity  of  substances  in  colloidal  solu- 
tion indicates  that  the  osmotic  pressure  in  such  a  case 
is  not  completely  defined  by  the  two  factors  concentration 
and  temperature.  It  is  probable,  as  already  suggested, 


COLLOIDAL   SOLUTIONS  .185 

that  the  extent  of  aggregation  of  the  colloid  depends 
to  some  extent  on  its  previous  history;  this  being  so, 
the  number  of  units  or  separate  aggregates  in  the 
solution,  and  therefore  also  the  osmotic  pressure,  would 
not  always  be  the  same  at  a  given  temperature. 

Striking  evidence  that  the  osmotic  activity  of  a  colloid 
depends  on  other  factors  than  concentration  and  tem- 
perature is  furnished  by  a  recent  investigation  of  the 
influence  exerted  by  electrolytes  on  the  osmotic  pressure 
of  colloidal  solutions.1  The  colloids  studied  in  this 
investigation  were  gelatin  and  egg  albumin,  and  the 
osmometer  used  consisted  of  a  flask-shaped  vessel  of 
collodion  provided  with  a  rubber  stopper  and  vertical 
glass  tube.  A  membrane  of  collodion  is  tough  and 
only  slightly  extensible ;  it  is  practically  impermeable 
to  gelatin  and  egg  albumin,  but  is  readily  permeable 
to  all  crystalloids.  With  this  apparatus  Lillie  deter- 
mined the  osmotic  pressure  exerted  by  a  colloid  (1) 
when  in  a  relatively  pure  condition,  (2)  when  in  the 
presence  of  crystalloids.  The  osmotic  effect  of  the 
crystalloid  in  the  latter  case  was  eliminated  by  adding 
it  also  to  the  liquid  outside  the  cell,  so  that  the  con- 
centrations of  the  crystalloid  on  the  two  sides  of  the 
membrane  were  equal.  It  was  then  found  that  the 
osmotic  activity  of  gelatin  and  egg  albumin,  while 
practically  uninfluenced  by  sucrose  and  other  non-electro- 
lytes, is  markedly  affected  by  electrolytes.  In  presence 
of  small  quantities  of  either  acid  or  alkali  the  osmotic 
pressure  of  a  gelatin  solution  is  notably  increased,  whilst 
that  of  an  egg  albumin  solution  is  slightly  lowered.  Salts, 
on  the  other  hand,  bring  about  a  lowering  of  osmotic 
activity  for  both  colloids,  the  magnitude  of  the  effect 
varying  with  the  concentration  and  the  nature  of  the 
salt.  This  may  be  illustrated  by  the  following  figures 
1  Lillie,  Amer.  Journ.  PhysioL,  1907,  2270,  1. 


186 


PHYSICAL   CHEMISTRY 


for  the  osmotic  pressure  of  1*25  per  cent,  egg  albumin 
and  gelatin  solutions  : — 


1-25  per  Cent. 
Salt 
Present. 

None   .     . 

Egg  Albumin. 
Osmotic  Pressure 
in  mm.  Hg. 

.     .      18-0 

1-25  pt 
Salt 
Present. 

None    . 

^NaCl   . 

.     .       6-8 

-?  NaCl 

N  KNQ 

96           3  ' 

IN.CI    . 

.     .      7-3 
.     .       3-25 

|NaBr 

96 

12           3' 

.     .      3-0 

—  NaNC 

Osmotic  Pressure 
in  mm.  Hg. 

.     5-9 

.     2-8 

.     3-1 
.     3'4 

3-0 


It  is  apparent,  then,  that  the  osmotic  activity  of  a 
colloid  at  a  given  concentration  varies  to  a  very  marked 
extent  with  the  nature  and  amount  of  crystalloid  present. 
The  lower  pressures  observed  for  egg  albumin  and  gelatin 
in  presence  of  salts  can  be  attributed  only  to  a  reduction 
in  the  number  of  colloid  units  or  aggregates  in  solution  ; 
so  that  the  effect  of  salts,  even  in  small  quantities,  is  to 
increase  the  aggregation  of  the  colloid.  This  is  perhaps 
only  natural,  for  it  must  be  borne  in  mind  that  the  addition 
of  large  quantities  of  salt  to  a  protein  solution  leads 
frequently  to  the  precipitation  of  the  protein ;  the 
increased  aggregation  brought  about  by  small  quantities 
of  salt  may  therefore  be  regarded  as  the  first  stage  in 
a  process  which  leads  ultimately  to  precipitation. 

Lillie's  investigation  indicates  also  that  the  pheno- 
menon of  hysteresis  occurs  in  connection  with  the  change 
in  the  aggregation  of  the  protein  which  accompanies 
change  in  the  amount  of  electrolyte  present.  The  state 
of  aggregation  induced  by  a  given  electrolyte  appears  to 
persist  to  some  extent  even  after  the  electrolyte  has  been 
removed,  and  it  is  at  least  possible  that  the  very  low 
values  recorded  by  Reid l  for  the  osmotic  pressure  of 

1  Loc.  dt. 


COLLOIDAL  SOLUTIONS  187 

protein  solutions  were  due  to  the  treatment  with  concen- 
trated salt  solutions  to  which  the  protein  was  subjected. 

The  influence  of  electrolytes  on  the  osmotic  behaviour 
of  colloids  has  been  strikingly  confirmed  by  a  recent 
study  of  congo  red.1  This  dye  may  be  regarded  as  a 
colloid,  inasmuch  as  it  does  not  diffuse  through  parch- 
ment paper :  in  an  electric  field  it  moves  towards  the 
anode,  and  it  is  precipitated  very  readily  by  di-  and  tri- 
valent  cations.  The  osmotic  activity  of  congo  red, 
measured  in  the  form  of  osmometer  described  by  Moore 
and  Roaf,  is  very  nearly  equal  to  that  calculated  on  the 
supposition  that  it  dissolves  as  single  molecules,  forming 
a  true  solution.  Bayliss  finds,  however,  that  the  theoreti- 
cal osmotic  pressure  can  be  obtained  only  in  the  complete 
absence  of  extraneous  electrolytes2;  even  the  carbon 
dioxide  present  in  ordinary  distilled  water  brings  about 
a  notable  fall  in  the  osmotic  pressure,  owing  to  the 
aggregation  of  molecules  to  particles. 

Molecular  Weight  of  Colloids. — As  has  already  been 
pointed  out  in  an  earlier  part  of  this  volume,  the  know- 
ledge of  the  osmotic  pressure  of  a  solution  enables  us  to 
calculate  the  molecular  weight  of  the  dissolved  substance. 
Such  a  calculation  is  based  on  the  assumption  that 
osmotic  pressure  is  proportional  to  concentration  and 
absolute  temperature.  As  shown,  however,  in  the  fore- 
going paragraphs,  concentration  and  temperature  are  not 
the  only  factors  which  determine  the  osmotic  pressure 
of  a  substance  in  colloidal  solution. 

It  is  therefore  futile  to  deduce  a  value  for  the  mole- 
cular weight  of  a  colloid  from  the  osmotic  pressure  of 
its  solution :  such  a  value  could  not  be  regarded  as  a 
characteristic  figure  for  the  colloid  in  question :  it  would 

1  Bayliss,  Proc.  Roy.  Soc.,  B,  1907,  81,  269. 

*  See  also  Biltz  and  Vegesack,  Zcit.  physical.  Chem.,  1909,  68,  357 ; 
1910,  73,  481;  Donnan  and  Harris,  Journ.  Chem.  Soc.,  1911,  99,  1554. 


188  PHYSICAL  CHEMISTRY 

have  reference  only  to  the  particular  conditions  of  the 
colloid  at  the  time  when  the  osmotic  pressure  was 
determined. 

Values  for  the  molecular  weight  of  substances  in 
colloidal  solution  may  be  deduced  also  from  their  effect  on 
the  vapour  pressure,  the  boiling  point,  and  the  freezing 
point  of  water.  Such  values,  however,  must  be  accepted 
with  reserve,  on  the  grounds  specified  in  the  foregoing 
paragraph.  There  is,  further,  a  special  reason  why  little 
reliance  can  be  placed  on  the  indirect  measurement  of 
osmotic  pressure  in  the  case  of  a  colloidal  solution.  If  P 
is  the  osmotic  pressure  of  an  aqueous  solution,  and  t  is 
the  extent  to  which  the  freezing  point  of  the  solution 
is  lower  than  that  of  water,  then,  as  shown  on  p.  110, 
P=  12'03£  atmospheres.  According  to  this  formula,  the 
freezing  point  of  a  solution  which  gives  an  osmotic 
pressure  of  50  mm.  of  Hg — an  easily  measurable 
quantity — would  be  only  about  0'005°  below  the  freezing 
point  of  water.  Such  a  small  temperature  difference 
might  easily  escape  detection  in  ordinary  work,  and  in 
any  case  the  experimental  error  in  its  determination  is 
relatively  large.  For  the  measurement,  therefore,  of  the 
osmotic  pressure  of  a  colloidal  solution  the  direct  method 
is  to  be  preferred.  The  values  frequently  quoted  for  the 
molecular  weight  of  such  colloids  as  dextrin,  glycogen, 
and  silicic  acid — values  based  on  the  determination  of 
the  freezing  point — have  a  very  limited  significance, 
partly  on  account  of  the  deficiencies  of  the  method  em- 
ployed, and  partly  on  account  of  the  variability  in  the 
aggregation  of  a  colloid  with  the  conditions. 

Colloids  in  an  Electric  Field. — Nearly  twenty  years 
ago  Linder  and  Picton  1  made  the  interesting  observation 
that  when  two  wires  connected  with  the  terminals  of 

1  Journ.  Chem.  Soc.,  1892,  61,  148. 


COLLOIDAL   SOLUTIONS  189 

a  battery  were  placed  in  a  colloidal  solution  of  arsenious 
sulphide  the  sulphide  was  attracted  by  the  positive  pole, 
and  was  gradually  transported  thither.  Ferric  hydroxide 
in  colloidal  solution  was,  on  the  other  hand,  attracted  by 
the  negative  pole.  It  appears,  therefore,  that  the  particles 
of  colloidal  arsenious  sulphide  carry  a  negative  electric 
charge,  while  those  of  colloidal  ferric  hydroxide  carry 
a  positive  charge.  The  behaviour  of  colloids  generally 
in  an  electric  field  has  been  extensively  studied,  and  it  is 
found  that,  as  a  rule,  they  carry  a  definite  charge.  In 
the  following  table  various  common  colloids  are  classified 
according  as  they  are  electro-positive  and  move  to  the 
cathode,  or  electro-negative  and  move  to  the  anode : — 

Electro-positive.  Electro-negati  ve. 

Ferric  hydroxide  Arsenious  sulphide 

Chromium  hydroxide  Silicic  acid 

Methylene  blue  Tannin 

Bismarck  brown  Caramel 

Haemoglobin  Starch 

Platinum 

Gold 

Indigo 

The  movement  of  colloids  in  an  electric  field  may  be 
demonstrated  with  the  help  of  the  apparatus  described 
on  p.  154.  The  bottom  of  the  U  tube  is  charged 
with  a  solution  of  caramel,  for  instance,  the  upper 
part  of  each  limb  being  occupied  by  distilled  water. 
When  platinum  wires  connected  with  the  terminals  of 
a  200-volt  circuit  are  put  in  the  water  of  the  two 
limbs,  it  is  obvious  after  a  long  time  that  the  column 
of  caramel  solution  has  fallen  in  one  limb  and  risen  in 
the  other.  If  the  wires  are  subsequently  tested,  it  will 
be  found  that  the  one  towards  which  the  caramel 
advances  is  connected  with  the  positive  terminal  of  the 
circuit.  A  similar  experiment  might  be  made  with 
any  of  the  colloids  mentioned  above. 


190  PHYSICAL  CHEMISTEY 

An  apparatus  of  the  same  kind  has  been  employed  1 
to  determine  the  actual  rate  at  which  colloidal  metals 
migrate  from  cathode  to  anode  under  the  action  of  an 
electric  force.  As  shown  by  Bredig,2  a  colloidal  solution 
of  platinum,  gold,  or  silver  can  be  prepared  by  producing 
a  small  electric  arc  between  wires  of  the  metal  in  question 
when  these  are  immersed  in  water.  The  passing  of  the 
discharge  between  the  ends  of  the  wires  brings  about 
what  is  known  as  the  '  electrical  pulverisation '  of  the 
metal ;  a  coloured  solution  is  obtained  in  each  case,  which 
can  be  filtered  without  change,  and  which  can  be  purified 
by  dialysis  from  any  electrolytic  impurities.  The 
solution  contains  an  appreciable  quantity  of  metal,  and 
is  analogous  in  its  properties  to  colloidal  solutions  of 
arsenious  sulphide,  ferric  hydroxide,  and  many  organic 
substances.  If,  now,  the  bend  of  the  U  tube  of  the 
apparatus  referred  to  in  the  previous  paragraph  is  filled 
with  a  colloidal  solution  of  platinum,  gold,  or  silver,  and 
the  upper  parts  of  the  two  limbs  contain  water  of  the 
same  specific  conductivity  as  the  colloidal  solution,  then 
when  wires  connected  with  a  battery  are  put  in  the  two 
water  columns  the  potential  gradient  is  uniform  through- 
out the  tube  ;  the  fall  of  potential  per  centimetre  is  known. 
Under  the  action  of  the  electric  force  the  colloidally  dis- 
solved metal  moves  towards  the  anode,  and  from  the 
distance  actually  traversed  in  a  given  time  the  velocity 
of  migration  may  be  calculated  for  the  potential  gradient 
prevailing  in  the  tube.  In  this  way  Burton  has  found 
that  for  a  potential  gradient  of  1  volt  per  cm.  the  velocity 
of  migration  of  colloidal  platinum,  gold,  and  silver  is 
about  0*0002  cm.  per  second,  which  is  rather  more  than 
one-third  of  the  rate  at  which  the  silver  ion  moves  under 
similar  conditions. 

1  Burton,  Phil.  Mag.,  1906,  11,  425. 

2  Zeit.  physical  Chem.^1899,  31,  258. 


COLLOIDAL   SOLUTIONS  191 

One  of  the  most  significant  facts  bearing  on  the  be- 
haviour of  colloids  in  an  electric  field  is  Hardy's 
observation1  that  protein  in  solution  may  be  either 
electro-positive  or  electro-negative,  according  to  circum- 
stances. Hardy  used  the  slightly  opalescent  fluid  ob- 
tained when  white  of  egg  is  mixed  with  8-9  times  its 
volume  of  water,  filtered  and  boiled:  this  fluid  is 
alkaline  in  reaction.  When  it  is  dialysed  against  dis- 
tilled water,  coagulation  occurs,  and  the  coagulum  may 
be  broken  up  and  suspended  in  distilled  water  without 
solution  taking  place.  If,  however,  a  trace  of  acid  is 
added,  the  flakes  of  the  coagulum  disappear,  and  an 
opalescent  fluid  with  acid  reaction  is  produced.  If  a 
current  is  passed  through  the  original  alkaline  fluid,  the 
protein  moves  from  cathode  to  anode  and  a  coagulum 
forms  round  the  anode,  while  if  a  current  is  passed 
through  the  acid  fluid  described  in  the  last  sentence,  the 
protein  moves  from  anode  to  cathode.  It  appears,  there- 
fore, that  in  an  alkaline  medium  the  protein  is  electro- 
negative, but  that  in  an  acid  medium  it  is  electro-positive. 
It  was  found,  further,  that  if  the  coagulum  obtained  by 
prolonged  dialysis  is  thoroughly  broken  up  and  suspended 
in  distilled  water,  no  movement  of  the  protein  particles 
occurs  in  an  electric  field.  If,  however,  the  coagulum 
formed  at  the  anode  by  passing  a  current  through  the 
original  alkaline  fluid  is  thoroughly  broken  up,  the 
particles  leave  the  anode  and  move  towards  the  cathode ; 
their  electrical  character  has  changed. 

Such  a  reversal  of  the  electric  charge  on  a  colloidal 
substance  has  been  observed  in  other  cases.  Burton, 
for  instance,  working  with  colloidal  solutions  of 
silver  and  gold,2  has  found  that  the  addition  of 
small  quantities  of  aluminium  sulphate  causes  first  a 

1  Journ.  PhysioL,  1899,  24,  288. 

2  Phil.  Mag.,  1906,  12,  472. 


192  PHYSICAL   CHEMISTKY 

decrease  in   the   charge  on   the  colloidal   particles,  and 
ultimately  a  reversal. 

Analogy  between  Colloidal  Solutions  and  Suspen- 
sions.— The  behaviour  of  substances  in  colloidal  solution 
when  exposed  to  the  action  of  electrical  forces  is  very 
similar  to  the  behaviour  of  suspensions  in  the  same 
circumstances.  With  the  apparatus  already  described, 
it  can  be  shown  that  when  a  current  is  passed  through 
suspensions  of  quartz  powder,  gum  mastic,  or  shellac, 
the  suspended  particles  move  towards  the  anode. 

A  great  deal  of  other  evidence  is  available  in  support 
of  the  view  that  there  is  a  close  relationship  between 
colloidal  solutions  and  ordinary  suspensions.  When  we 
speak  of  a  *  suspension '  we  may  think  of  a  fluid,  in 
which  distinguishable  particles  are  floating  about.  There 
are,  however,  all  grades  of  suspensions ;  many  of  them 
can  be  filtered  without  alteration,  and  in  many  cases 
no  individual  particles  can  be  detected  with  the  naked 
eye:  the  microscope  at  least  is  required  to  render  the 
suspended  particles  visible.  But  if  all  the  optical 
methods  available  for  the  recognition  of  the  non-homo- 
geneous character  of  a  liquid  are  applied  to  colloidal 
solutions,  evidence  is  obtained  that  these  also  contain 
distinct  particles. 

One  of  these  methods  consists  in  the  application  of 
the  Tyndall  test.  It  is  well  known  that  if  a  beam  of 
light  enters  a  darkened  room  in  which  dust  particles 
are  floating  its  path  is  rendered  evident  by  the  scattering 
of  the  light  at  the  surface  of  the  particles ;  each  one 
of  these  appears  as  a  bright  moving  speck.  Similarly, 
when  a  powerful  beam  of  light  passes  through  a  vessel 
containing  a  suspension,  say,  of  fine  silver  chloride 
particles  in  water,  its  path  is  rendered  evident  by  the 
scattering  of  the  light  which  takes  place  at  the  surface 


COLLOIDAL  SOLUTIONS  193 

of  the  suspended  particles ;  further,  the  light  which  is 
scattered  is  partly  polarised.  If,  on  the  other  hand, 
the  beam  is  passed  through  a  solution  which  is  perfectly 
free  from  all  suspended  particles,  no  scattering  of  the 
light  takes  place,  and  the  path  of  the  beam  cannot  be 
detected ;  such  a  solution  is  described  as  '  optically 
empty.'  Now  the  Tyndall  phenomenon,  that  is,  the 
appearance  of  opalescence  which  is  observed  when  a 
powerful  beam  of  light  is  passed  through  a  fluid  con- 
taining definite  suspended  particles,  is.  exhibited  also 
by  the  majority  of  colloidal  solutions.  Picton  and 
Linder,1  for  instance,  describe  a  colloidal  solution  of 
ferric  hydroxide  which,  examined  under  a  powerful 
microscope,  appeared  to  be  perfectly  homogeneous,  and 
which  yet  betrayed  the  track  of  a  beam  of  light  very 
distinctly,  the  light  being  completely  polarised.  A  clear 
solution  of  haemoglobin,  similarly  examined,  gave  a  dis- 
tinct soft  luminous  beam,  the  light  of  which  was  com- 
pletely polarised.  A  positive  result  is  obtained  also  with 
solutions  of  such  substances  as  dextrin  and  gum  arable 
in  water. 

The  extent  of  the  analogy  which  thus  appears  to 
exist  between  suspensions  and  colloidal  solutions  has 
been  thoroughly  tested  in  recent  years  with  the  help 
of  the  ultramicroscope,  as  devised  by  Zsigmondy  and 
Siedentopf.2  The  usefulness  of  this  instrument  depends 
on  the  Tyndall  phenomenon,  but  whereas  the  power 
of  any  solution  to  exhibit  the  Tyndall  phenomenon 
permits  merely  the  conclusion  that  the  solution  contains 
distinct  individual  particles,  the  ultramicroscope  makes 
it  possible  to  detect  the  individual  particles  themselves, 
even  where  the  most  powerful  microscope  has  failed 
to  reveal  any  trace  of  heterogeneity.  In  the  ultra- 

1  Journ.  Chem.  Soc.,  1892,  61,  148. 

2  See  Zsigmondy 's  Colloids  and  the  Ultramicroscope,  p.  103. 


194  PHYSICAL  CHEMISTRY 

microscope  provision  is  made  for  focussing  an  intense 
beam  of  light  in  the  liquid  under  examination,  and  in 
viewing  the  beam  at  right  angles  to  its  direction  by 
a  microscope.  Any  particles  suspended  in  the  liquid 
are  then  revealed  in  the  field  of  the  microscope  as 
bright  moving  discs  on  a  dim  background. 

The  power  of  the  ultramicroscope  to  detect  discrete 
particles  is  considerably  greater  than  that  obtainable  in 
ordinary  microscopic  methods.  Particles  of  less  than 
140  x  10~6  mm.  diameter  are  as  a  rule  not  visible  under 
the  microscope  (compare  the  wave-length  of  red  light, 
which  is  about  700  x  10  ~6  mm.),  but  with  the  ultra- 
microscope  particles  in  a  solution  of  colloidal  gold  as 
small  as  4xlO~6  mm.  have  been  detected.  One  way 
in  which  the  size  of  the  particles  revealed  by  the  ultra- 
microscope  may  be  estimated  has  recently  been  de- 
scribed by  Burton,1  and  some  figures  may  be  quoted 
showing  the  method  adopted  by  this  investigator.  A 
solution  of  colloidal  silver  containing  6-8  mg.  of  silver 
in  100  cub.  cm.  was  diluted  with  water  to  100  times 
its  original  volume.  With  the  help  of  the  ultramicro- 
scope the  number  of  particles  in  O'l  cub.  mm.  of  the 
diluted  solution  was  found  to  be  300.  Hence  in  1  cub.  cm. 
of  the  original  solution  there  must  have  been  3  x  108 
particles  weighing  6*8xlO~5  gram.  If  it  is  assumed 
that  the  particles  are  spherical  and  that  their  specific 
gravity  is  10*5,  then  the  mean  radius  is  1'TxlO"5  cm. 
From  experiments  with  colloidal  platinum,  gold,  and  silver, 
Burton  found  as  the  average  diameter  of  the  particles  in 
these  cases  2  x  10~5  -  6  X  10~5  cm.  It  is  interesting  to 
note  that  the  smallest  particle  which  can  be  detected  in 
the  ultramicroscope  under  the  most  favourable  conditions 
(with  bright  sunshine)  is  about  ten  times  as  great  as  an 

1  Phil.  Mag.,  1906,  11,  425.  For  a  review  of  the  methods  used  in 
determining  the  size  of  colloidal  particles,  see  Henri,  Zeit.  Chem.  Ind. 
KoUoide,  1913,  12,  246. 


COLLOIDAL  SOLUTIONS  195 

average  chemical  molecule,  calculation  having  shown  that 
the  diameter  of  a  chloroform  molecule  is  about  08  x  10~6 
mm.,  that  of  an  ethyl  alcohol  molecule  about  0'4xlO~6, 
and  that  of  a  hydrogen  molecule  about  01  X  10~6. 

The  great  majority  of  colloidal  solutions,  when  ex- 
amined in  the  ultramicroscope,  are  found  to  contain 
distinct  particles.  Cases  are  on  record,  however,  in 
which  the  ultramicroscopic  examination  of  colloidal  solu- 
tions showed  them  to  be  optically  empty.  Zsigmondy, 
for  instance,  prepared  a  colloidal  solution  of  gold  which 
could  not  be  shown  to  contain  discrete  particles.  Such 
observations  warn  us  that,  while  there  is  good  ground 
for  regarding  suspensions  and  colloidal  solutions  as 
being  closely  allied,  no  hard-and-fast  line  of  division 
can  be  drawn  on  the  other  hand  between  colloidal  and 
crystalloidal  solutions.  For  while,  as  already  explained 
colloidal  solutions  can  be  prepared  which  are  optically 
empty,  there  are  solutions  of  crystalloids,  sucrose,  for 
instance,  which  cannot  be  obtained  in  this  condition, 
however  carefully  they  have  been  freed  from  suspended 
matter.1  Strictly  speaking,  we  must  from  the  mole- 
cular standpoint  regard  all  solutions  as  being  ultimately 
non-homogeneous,  and  it  is  due  to  the  inadequacy  of 
our  optical  apparatus  that  we  are  unable  to  recognise 
separate  particles  in  a  dilute  aqueous  solution  of  ethyl 
alcohol  or  sodium  chloride.  One  observation  bearing 
directly  on  the  question  of  the  homogeneity  of  crystal- 
loidal solutions  has  been  recorded  by  van  Calcar  and 
Lobry  de  Bruyn,2  who  found  that  by  rapidly  centrifu- 
galising  sucrose  solutions  differences  in  concentration 
could  be  induced.  Similar  treatment  of  a  saturated 
solution  of  sodium  sulphate  led  to  the  crystallisation  of 
some  of  the  salt. 

1  Lobry  de  Bruyn  and  Wolff,  Rec.  trav.  chim.,  1904,  23,  155. 
8  Rec.  trav.  chim.,  1904,  23,  218. 


196  PHYSICAL  CHEMISTRY 

The  inadvisability  of  attempting  to  put  suspensions, 
colloidal  solutions,  and  crystalloidal  solutions  in  three 
absolutely  distinct  classes  is  emphasised  by  the  fact 
that  it  is  possible  to  prepare  colloidal  solutions  of  one 
and  the  same  substance  of  all  degrees  of  heterogeneity. 
Linder  and  Picton,1  in  their  study  of  colloidal  solutions 
of  arsenious  sulphide,  showed  that  various  '  grades '  of 
solution  could  be  obtained,  according  to  the  method  of 
preparation. 

They  describe  and  distinguish  the  following : — 

(a)  Contained  aggregates  which  were  visible  under  the 
microscope. 

(/:?)  Was  free  from  microscopically  visible  particles, 
but  diffusion  of  the  particles  did  not  occur. 

(7)  Contained  invisible  particles  which  diffused,   but 

were  kept  back  by  filtration  through  a  porous 
pot. 

(8)  Contained   invisible  particles  which   diffused  and 

were  capable  of  passing  through  a  porous  pot. 

The  solution,  however,  scattered  and  polarised 

a  beam  of  light. 

This  example  shows  how  far  it  is  possible  to  vary 
the  extent  of  aggregation  of  one  and  the  same  sub- 
stance in  colloidal  solution.  If  it  was  a  question  of 
deciding  whether  a  given  arsenious  sulphide  solution 
was  really  a  colloidal  solution  or  only  a  suspension,  the 
verdict  would  depend  on  the  criterion  of  homogeneity 
employed:  a  solution  which,  according  to  one  test,  was 
a  true  colloidal  solution  would,  according  to  another 
test,  be  merely  a  suspension.  It  is  obvious,  therefore, 
that,  while  there  are  no  doubt  broad  distinctions  to 
be  drawn  between  suspensions,  colloidal  solutions,  and 
crystalloidal  solutions,  the  one  class  merges  gradually 
into  the  other.  The  size  of  the  individual  particle 

1  Loo.  dt. 


COLLOIDAL  SOLUTIONS  197 

present  in  a  solution  increases  without  any  noticeable 
break  from  that,  say,  of  an  alcohol  molecule  in  water, 
through  that  of  the  carbohydrates  and  proteins  in 
aqueous  solution,  to  cases  where  the  individual  particles 
are  so  large  that  we  speak  of  them  as  '  suspended.' 

Brownian  Movement. — The  invention  of  the  ultra- 
microscope  and  the  study  of  the  phenomena  exhibited 
by  colloidal  solutions  have  directed  attention  afresh  to 
an  observation  which  was  made  nearly  a  century  ago 
by  the  botanist  Robert  Brown,  and  which  has  since 
then  been  the  subject  of  repeated  investigation.  With 
the  aid  of  the  microscope  Brown  observed  that  fine 
particles  suspended  in  water,  such  as  gamboge  or  fat 
particles  from  milk,  executed  a  vibratory  movement  about 
a  mean  position.  This-  movement  has  been  shown  to 
be  independent  of  any  temporary  forces  due  to  slight 
differences  of  temperature  or  concentration;  so  long  as 
the  particles  float  in  the  liquid,  the  movement  con- 
tinues without  ceasing. 

The  ultramicroscope  has  revealed  the  fact  that  a 
colloidal  solution  containing  particles  much  smaller  than 
Brown  was  able  to  observe  is  the  scene  of  still  greater 
activity.  Zsigmondy,  describing  the  movement  of  the 
gold  particles  in  a  gold  hydrosol,  compares  them  to  a 
s  war  in  of  dancing  gnats.  The  finer  the  particles,  the 
more  rapid  is  their  movement ;  with  increase  in  size 
the  movement  becomes  slower,  and  it  is  ultimately 
imperceptible  when  the  diameter  of  the  particles  is 
about  0*004  mm.  Zsigmondy  considers  that  in  contra- 
distinction to  the  typical  Brownian  movement  about  a 
mean  position,  the  motion  of  the  smallest  gold  particles 
in  a  gold  hydrosol  is  continuous  ;  an  individual  particle, 
after  moving  about  in  a  zigzag  fashion,  may  suddenly 
rush  across  the  field  like  a  living  thing.  The  mean 


198  PHYSICAL  CHEMISTRY 

free  path  is  therefore  considerably  greater  in  the  case 
of  the  smallest  gold  particles  than  it  is  in  the  ordinary 
Brownian  movement,  but  there  is  no  doubt  that  the 
phenomenon  is  essentially  the  same  in  the  two  cases. 

The  problem  has  recently  been  attacked  by  Svedberg,1 
who  has  prepared  a  number  of  colloidal  solutions  of 
platinum  in  various  media  and  shown  that  the  amplitude 
of  vibration  of  the  particles  is  nearly  inversely  pro- 
portional to  the  viscosity  of  the  medium.  The  mean 
velocity,  however,  of  a  platinum  particle  of  given  size 
is  practically  constant ;  for  a  particle  weighing  about 
2-5  x  10~15  gram  the  mean  velocity  is  estimated  to  be 
3  X  10~2  cm.  per  second  at  the  ordinary  temperature. 
Comparison  of  these  figures  with  the  corresponding  ones 
given  by  Ramsay2  for  larger  particles  leads  to  a  cal- 
culation of  the  velocity  with  which  a  platinum  molecule 
would  move.  It  is  noteworthy  that  the  value  so  cal- 
culated is  in  agreement  with  the  value  based  on  the 
assumptions  of  the  kinetic  theory.  It  is  therefore 
probable  that  the  Brownian  movement  of  suspended  or 
colloidal  particles  is  an  expression  of  the  molecular 
movement  which  is  attributed  to  matter  generally.  This 
view  has  been  strengthened  by  still  more  recent  work, 
both  theoretical  and  experimental.3  Indeed  Ostwald 4 
has  expressed  the  opinion  that  the  agreement  between 
the  observed  and  calculated  values  for  the  rate  of 
movement  of  a  suspended  particle  is  so  close  as  to 
amount  to  an  experimental  proof  of  the  kinetic  nature 
of  heat. 

Filtration  of  Colloidal  Solutions. — Filtration  is  the 

1  Zcit.  Elektrochem.,  1906,  12,  853. 

2  Chem.  News,  1892,  65,  90. 

3  See  Svedberg,  Zeit.  Elektrochem.,  1906,  12,  909  ;  Perrin,  Compt.  rend., 
1908,  146,  967  ;  147,  475,  530  ;  also  Perrin's  Broivnian  Movement  and 
Molecular  Reality  (1910). 

4  Grundriss  der  allgcmeinen  Chcmie  (1909),  p.  543. 


COLLOIDAL   SOLUTIONS  199 

time-honoured  method  of  freeing  a  liquid  from  suspended 
particles,  and  the  remarkable  similarity  between  sus- 
pensions and  colloidal  solutions  leads  us  naturally  to 
inquire  how  far  this  method  is  efficient  when  applied 
to  colloidal  solutions.  The  inquiry  really  reduces  itself 
to  the  question  whether  we  can  procure  filters  with 
sufficiently  small  pores.  The  analytical  chemist  knows 
that  the  possibility  of  filtering  a  very  finely  divided 
precipitate  depends  on  the  texture  of  the  filter  paper. 
In  the  case  of  colloidal  solutions,  which  pass  unchanged 
through  the  finest  filter  paper,  the  possibility ^jf  a 
mechanical  separation  of  the  colloid  depends  on  the 
discovery  of  a  filter  with  exceedingly  small  pores — 
of  a  diameter  1  x  10~6  —  40  x  10~6  mm.  One  such,  as 
suggested  by  Martin,  is  obtained  by  impregnating  the 
pores  of  a  Pasteur-Chamberland  candle  with  gelatin. 
A  filter  so  prepared  is  highly  permeable  to  crystalloids 
such  as  sodium  chloride  and  butyric  acid,  but  is  very 
slightly  permeable  to  colloids  such  as  ferric  hydroxide 
and  soluble  starch,1  so  that  if  a  colloidal  solution  of 
ferric  hydroxide  is  filtered  under  100  ^  atmospheres 
pressure  in  such  an  apparatus  the  filtrate  consists  of 
practically  pure  water.  The  permeability  of  such  a 
filter  to  certain  colloids  increases  as  the  concentration 
of  the  impregnating  gelatin  solution  diminishes.  This 
fact  has  been  utilised  in  the  attempts  which  have 
recently  been  made  to  differentiate  between  various 
colloidal  solutions  by  means  of  graded  filters.  These, 
according  to  Bechhold's  suggestion,2  may  be  prepared 
(1)  by  impregnating  filter  paper  with  a  solution  of 
collodion  in  glacial  acetic  acid  and  then  dipping  in 
water,  or  (2)  by  soaking  filter  paper  in  gelatin  solution 
and  then  hardening  with  formaldehyde.  The  size  of 

1  See  Craw,  Proc.  Roy.  Soc.,  B,  1906,  77,  311. 

2  Zeit.  physikal.  Chem.,  1907,  60,  257. 


200  PHYSICAL   CHEMISTRY 

the  pores  in  such  gelatinised  filters  diminishes  as  the 
concentration  of  collodion  or  gelatin  used  in  their  pre- 
paration increases.  A  series  of  graded  filters  is  thus 
obtainable  which  may  be  used  to  sort  out  a  number 
of  colloidal  solutions  according  to  the  size  of  particles 
they  contain.  It  is  true  that  the  pores  in  a  filter  are 
not  all  of  equal  diameter  and  that  the  particles  in  a 
colloidal  solution  vary  in  size,  but  still  it  is  possible 
to  discover  for  a  given  colloidal  solution  which  one  of 
the  series  of  filters  is  just  able  to  prevent  the  passage 
of  the  colloid.  Such  experiments  obviously  lead  to  a 
classification  of  colloidal  solutions  according  to  the 
size  of  the  particles  they .  contain,  and  the  following- 
table  given  by  Bechhold  is  based  on  work  of  this  kind : 1 — 


Suspensions 

Prussian  Blue 

Colloidal  Platinum 

Colloidal  Ferric  Hydroxide 

Casein  (in  Milk) 

Colloidal  Arsenious  Sulphide 

Colloidal  Gold  (40X  10~6  mm.) 

1  per  cent.  Gelatin 

1  per  cent.  Haemoglobin 


Serum  Albumin 

Diphtheria  Toxin 

Protalbumose 

Colloidal  Silicic  Acid 

Deuteroalbumose 

Litmus 

Dextrin 

Crystalloids 


Although  the  value  of  this  table  is  qualified  by  the 
fact  that  the  size  of  the  particles  in  the  colloidal 
solution  of  a  given  substance  varies  with  the  mode  of 
preparation,  yet  the  order  given  is  in  general  agreement 
with  theoretical  considerations  and  with  the  results  of 
ultramicroscopic  investigation. 

1  The  pressures  under  which  filtration   took   place  in  Bechhold's 
experiments  were  between  0'2  and  5  atmospheres. 


CHAPTER  X 

THE  SEPARATION  OF  COLLOIDS  FROM  THEIR 
SOLUTIONS 

Suspension  and  Emulsion  Colloids. — In  the  foregoing 
chapter  a  good  deal  of  evidence  has  been  brought 
forward  showing  that  the  region  of  colloidal  solution 
adjoins  that  of  true  solution  on  the  one  side  and  that 
of  suspensions  on  the  other.  When  now  we  consider 
the  influences  which  bring  about  a  separation  of  the 
colloid  from  its  solution,  it  is  found  that  the  substances 
which  form  colloidal  solutions  may  be  divided  into  two 
classes.  In  relation  to  .  precipitating  or  coagulating 
agents  the  one  class  resembles  suspensions,  while  the 
other  behaves  more  like  crystalloidal  substances. 

The  two  classes  are  those  which  have  already  been 
referred  to  (p.  178)  as  irreversible  and  reversible  colloids ; 
they  may  be  distinguished  also  as  '  suspension  colloids ' 
and  'emulsion  colloids,'  or  as  ' suspensoids '  and  'emul- 
soids.' 1  A  colloid  belonging  to  the  suspensoid  class 
gives  with  water  a  mixture  which  is  non-viscous  and 
non-gelatinising,  but  is  coagulated  on  the  addition  of 
small  quantities  of  electrolytes.  A  colloid  belonging 
to  the  emulsoid  class  gives  with  water  a  mixture  which 
is  viscous,  gelatinises,  and  is  not  readily  coagulated  by 
salts. 

The  Coagulation  of  Suspensoids. — One  of  the  most 
characteristic  features  of  a  colloidal  solution  of  arsenious 

1  von  Weimarn,  Zeit.  Chem.  2nd.  Kottoide,  1908,  3,  26. 


202  PHYSICAL  CHEMISTRY 

sulphide  or  ferric  hydroxide  is  the  ease  with  which  these 
colloids  are  precipitated  on  the  addition  of  electrolytes. 
A  similar  sensitiveness  to  small  quantities  of  salts  is 
exhibited  by  suspensions.  Bodlander  has  shown  that 
the  sedimentation  of  kaolin  suspensions  is  accelerated 
by  the  addition  of  electrolytes,  and  Hardy  has  found1 
that  a  suspension  of  gum  mastic  in  water,  prepared 
by  adding  a  dilute  alcoholic  solution  of  the  gum  to 
distilled  water,  is  precipitated  immediately  by  very  small 
quantities  of  magnesium  sulphate  or  barium  chloride. 
On  the  other  hand,  the  stability  of  a  suspension  or  the 
solution  of  a  suspensoid  is  practically  unaffected  by  the 
addition  of  a  non- electrolyte. 

In  making  a  comparative  study  of  the  influence  of 
various  electrolytes  in  causing  precipitation  of  suspen- 
soids,  it  is  necessary  to  follow  a  strictly  uniform  pro- 
cedure. Experience  has  shown,  firstly,  that  an  amount 
of  salt  which  is  not  capable  of  causing  immediate  coagula- 
tion is  nevertheless  effective  after  a  certain  interval, 
and  secondly,  that  the  total  quantity  of  electrolyte 
required  to  bring  about  complete  coagulation  of  the 
suspensoid  varies  according  as  the  electrolyte  is  added 
all  at  once  or  in  several  portions  successively.  We  have 
here  an  indication  of  the  part  which  the  time  factor  plays 
in  the  behaviour  of  colloidal  solutions  (compare  p.  184). 
In  order  to  avoid  complications  arising  from  these  causes 
Freundlich  has  suggested  the  following  procedure  : 2 — 2 
cub.  cm.  of  the  electrolytic  solution  are  added  to  20  cub.  cm. 
of  the  suspensoid  solution,  the  latter  being  well  shaken 
during  the  addition ;  the  mixture  is  then  allowed  to 
stand  for  two  hours,  after  which  time  a  few  cubic  centi- 
metres are  filtered  off,  and  the  filtrate  is  examined,  chemically 
or  colorimetrically,  for  the  suspensoid. 

1  Zeit.  pJiysikal.  Chem.,  1900,  33,  385. 
8  Ibid.,  1903,  44,  131. 


THE   SEPARATION   OF  COLLOIDS         203 

The  following  table  records  some  of  the  results  ob- 
tained by  Freundlich  in  his  investigation  of  the  in- 
fluence of  electrolytes  in  precipitating  a  colloidal  solution 
of  arsenious  sulphide.  The  tests  were  carried  out  as 
described  in  the  previous  paragraph,  and  the  numbers 
given  in  the  table  represent  the  minimum  concentration 
for  each  electrolyte  which  brought  about  coagulation  in 
two  hours  ;  the  figure  given  in  each  case  is  the  concen 
tration  of  the  electrolyte  after  mixing  with  the  arsenious 
sulphide  solution. 


NaCl 71-2 

KN03 69-8 

£K2SO4 91-5 

NH4C1  ......  59-1 

HC1  42-9 

MgCl2                 i        ~.        .  TOO 

MgSO4 1-13 

Oa(N03)a 0-95 

BaCl2 0-96 

ZnS04 1-13 

A1C13 .  '.        '.        .        '.        '.        '.  0-13 

A1(NO3)3 0-14 

0-13 


Inspection  of  this  table  shows,  firstly,  that  exceedingly 
small  quantities  of  electrolytes  suffice  to  cause  the  coagu- 
lation of  arsenious  sulphide  solutions ;  secondly,  and  more 
particularly,  that  the  coagulating  power  of  an  electrolyte 
in  relation  to  arsenious  sulphide  is  mainly  determined 
by  the  valency  of  the  cation.  The  higher  the  valency 
of  the  cation,  the  smaller  is  the  quantity  of  electrolyte 
required  to  bring  about  coagulation. 

Equally  striking  is  the  comparative  influence  of  salts 
in  bringing  about  the  coagulation  of  colloidal  ferric 
hydroxide.  This  is  shown  by  the  following  table, 


204  PHYSICAL  CHEMISTRY 

the  figures  in  which  have  the  same  significance  as  those 
quoted  in  the  previous  table.  It  is  evident  that  in 
relation  to  colloidal  ferric  hydroxide  the  coagulating 
power  of  a  salt  is  mainly  determined  by  the  valency 
of  the  negative  ion  ;  the  valency  of  the  positive  ion  is 
here  relatively  unimportant. 


NaOl  .......  9-25 

|Ba012        ......  9-64 

KN03         ......  11-9 

£Ba(NQ3)2  ......  14-0 

K2SO4         ......      0-20 

MgSO4        ......      0-22 

K2Cr2Or      ......      0-19 

The  contrast  in  this  respect  between  colloidal  arsenious 
sulphide  and  colloidal  ferric  hydroxide  becomes  still 
more  interesting  when  it  is  borne  in  mind  that  the 
colloidal  particles  of  arsenious  sulphide  are  negatively 
charged,  while  those  of  ferric  hydroxide  are  positively 
charged.  The  full  significance  of  this  was  first  appre- 
ciated by  Hardy,1  who  formulated  the  rule  that  the 
ion  of  an  electrolyte  which  determines  the  coagulation 
of  a  colloidal  solution  is  the  one  which  has  a  charge 
opposite  in  sign  to  that  on  the  colloidal  particles.  The 
validity  of  this  rule  is  strikingly  confirmed  by  Hardy's 
experiments  on  the  coagulation  of  the  protein  solution 
described  on  p.  191.  It  will  be  remembered  that  in  a 
faintly  alkaline  medium  this  protein  is  electro-negative, 
while  in  a  faintly  acid  medium  it  is  electro-positive.  It 
is  accordingly  found  that  in  presence  of  a  trace  of 
alkali  aluminium  sulphate  is  much  more  effective  than 
sodium  sulphate  in  bringing  about  the  coagulation  of 
the  protein,  while  magnesium  sulphate  occupies  an  in- 

1  Zeit.  physical.  Chem.,  1900,  33,  385. 


THE   SEPARATION  OF   COLLOIDS        205 

termediate  position ;  when,  however,  the  protein  solution 
contains  a  trace  of  acetic  acid,  the  three  sulphates  are 
about  equally  effective  in  causing  coagulation.  Similarly 
it  is  found  that  while  barium  chloride  is  more  effective 
than  sodium  sulphate  in  coagulating  the  electro-negative 
protein,  the  positions  of  the  salts  are  reversed  in  relation 
to  the  electro-positive  protein. 

All  these  results,  taken  in  conjunction  with  the  fact 
that  non-electrolytes  are  ineffective,  show  that  the  coagu- 
lation of  suspensoids  is  essentially  a  process  in  which 
ions  are  primarily  involved.  It  is  therefore  not  sur- 
prising to  find  that  when  various  electrolytes  all  yield- 
ing the  same  cation  are  used  to  coagulate  arsenious 
sulphide,  the  effectiveness  increases  with  the  degree 
of  dissociation ;  the  smaller  the  extent  to  which  the 
electrolyte  is  dissociated,  the  greater  relatively  is  the 
quantity  of  it  required  to  bring  about  complete  coagu- 
lation. This  is  shown  in  a  general  way  by  the  following 
table  ;  x  the  figures  in  the  second  column  give  the  con- 
centration necessary  in  each  case  to  cause  coagulation 
of  a  colloidal  arsenious  sulphide  solution  : — 

ApiH  Gram-Equivalents         Spec.  Conductivity 

per  Litre.  at  18°  (comparative). 

HC1  0-0038  14-5 

HNO3  0-0038  14-3 

H2SO4  0-0043  13-2 

H2C2O4  0-009  14-4 

H3PO4  0-015  13-9 

CH3.COOH  0-70  12-6 

It  is  seen  that  although  very  different  quantities  of 
the  acids  must  be  taken  to  bring  about  coagulation, 
yet  each  of  the  coagulating  solutions  has  approximately 
the  same  conductivity,  that  is,  approximately  the  same 
number  of  ions. 

If  the  coagulation  of  a  suspensoid  is  the  result  of  a 

1  Hardy,  loc.  cit. 


206  PHYSICAL   CHEMISTRY 

neutralisation  of  electric  charges,  one  on  the  colloid 
particles  and  one  on  the  coagulating  ion,  then  the  pre- 
cipitated colloid,  the  'coagulum,'  or  '  hydrogel '  as  it 
may  be  called,  ought  to  contain  either  the  acidic  or 
basic  part  of  the  added  electrolyte.  This  is  actually 
the  case ;  Linder  and  Picton 1  found  that  when  a 
colloidal  solution  of  arsenious  sulphide  is  precipitated 
by  adding  barium  chloride,  the  coagulum  contains 
barium.  This  barium  cannot  be  removed  from  the 
precipitate  by  continued  washing  with  water,  but  when 
the  precipitate  is  treated  for  some  time  with  a  solution 
of  another  salt,  the  barium  is  replaced  by  the  metallic 
part  of  this  salt.  Similar  observations  have  been  made 
by  Whitney  and  Ober,2  who  show  that  when  colloidal 
arsenious  sulphide  is  precipitated  by  barium  chloride, 
the  quantity  of  barium  carried  down  in  the  coagulum 
is  independent  of  the  concentration  of  the  solution,  but 
is  proportional  to  the  amount  of  sulphide  precipitated. 
The  composition  of  the  coagulum  obtained  by  Whitney 
and  Ober  is  represented  by  90As2S3  +  IBa,  and  in  pro- 
portion as  the  coagulum  retains  barium  the  filtrate 
becomes  acid.  Further,  when  four  equal  quantities  of 
colloidal  arsenious  sulphide  are  precipitated  by  barium, 
strontium,  calcium,  and  potassium  chloride  respectively, 
the  coagula  retain  equivalent  quantities  of  the  four 
metals.  The  retention  of  the  precipitating  metal  by 
the  coagulum  appears  to  be  a  case  of  adsorption,3  which 
will  be  discussed  later. 

Some  interesting  observations  are  on  record  dealing 
with  the  coagulation  of  colloidal  arsenious  sulphide  by 
mixed  electrolytes.  The  coagulating  effect  of  the  mixed 
chlorides  of  two  uni-valent  metals  is  simply  the  sum  of 
the  two  separate  effects ;  the  effect,  however,  of  a 

1  Journ.  Chem.  Soc.,  1895,  67,  63.       2  Zeit.  physical.  Chem.,  1902,39,  63. 
3  Freundlich,  Zeit.  physikal.  Chem,.,  1910,  73,  385. 


THE   SEPAEATION   OF  COLLOIDS        207 

mixture  containing  the  chloride  of  a  uni-valent  metal 
and  the  chloride  of  a  di-valent  metal,  is  less  than  that 
calculated  on  the  additive  basis.  There  appears,  there- 
fore, to  be  a  certain  antagonism  in  this  respect  between 
uni-valent  and  di-valent  cations,  and  it  is  worth  noting 
that  a  similar  antagonism  has  been  observed  in  some 
physiological  experiments  made  by  J.  Loeb.1  This  in- 
vestigator found  that  freshly  fertilised  eggs  of  Fwndulus 
heteroditus  when  transferred  from  sea-water  to  an  iso- 
tonic  solution  of  pure  sodium  chloride  all  die  without 
developing.  If,  however,  there  is  first  added  to  the  pure 
sodium  chloride  a  small  quantity  of  the  chloride  of  almost 
any  di-valent  metal,  the  resulting  mixture  is  a  more  or 
less  suitable  medium  for  the  development  of  fertilised 
Fundulus  eggs.  The  toxic  effect  of  pure  sodium  chloride 
is  thus  inhibited  by  salts  with  di-valent  cation. 

In, the  previous  chapter  it  was  suggested  (see  p.  186) 
that  the  increased  aggregation  of  a  colloid  brought  about 
by  small  quantities  of  a  salt  might  be  regarded  as  the  first 
stage  in  a  process  which  ultimately  leads  to  precipitation. 
Now  the  precipitation  of  a  positive  colloid,  as  we  have  just 
seen,  is  determined  chiefly  by  the  negative  ion  of  the 
added  electrolyte,  and  the  precipitation  of  a  negative 
colloid  by  the  positive  ion  of  the  added  electrolyte.  It 
might  therefore  be  expected  that  the  addition  of  an 
alkali  (i.e.  of  OH'  ions)  to  the  solution  of  a  positive 
suspensoid  in  quantity  insufficient  to  produce  coagulation 
would  lead  to  an  increase  in  the  size  of  the  suspensoid 
particles,  and  that  a  similar  result  would  follow  the 
addition  of  an  acid  (i.e.  of  H*  ions)  to  a  negative  sus- 
pensoid in  quantity  insufficient  to  produce  coagulation. 
This  has  been  verified  by  Mayer,  Schaeffer,  and  Terroine,2 
who  used  the  ultramicroscope  to  study  the  changes  of 

1  Amer.  Journ.  Physiol.,  1902,  6,  411.     Compare  Osterhout,  Science, 
1911,  34,  187;  1912,35,  112. 

8  Compt.  rend.,  1907,  145,  918. 

9 


208  PHYSICAL  CHEMISTRY 

size  exhibited  by  the  colloid  particles.  They  found 
further  that  the  addition  of  H*  ions  in  small  quantity 
to  a  positive  colloid  led  to  a  decrease  in  the  size  of  the 
particles,  as  did  also  the  addition  of  OH'  ions  to  a  negative 
colloid.  The  colour  changes  exhibited  by  gold  and  silver 
hydrosols  on  the  addition  of  minute  quantities  of  electro- 
lytes are  similarly  to  be  referred  to  alterations  in  the 
aggregation  of  the  colloid  particles. 

Reciprocal  Coagulation  of  Suspensoids. — The  study 
of  the  influence  of  electrolytes  on  suspensoids  has  shown 
clearly  that  in  the  process  of  coagulation  the  charge  on  the 
colloid  is  neutralised  by  that  on  one  of  the  ions  of  the 
added  electrolyte.  If  this  view  of  the  coagulation  pro- 
cess is  correct,  then  we  may  fairly  expect  that  if  we 
neutralise  the  charge  on  the  colloid  in  any  other  way, 
a  similar  result  will  follow.  In  the  previous  chapter 
evidence  has  been  recorded  showing  that  some  colloid- 
ally  dissolved  substances  carry  a  negative  charge,  while 
others  carry  a  positive  charge.  It  may  therefore  be  reason- 
ably expected  that  if  the  solution  of  a  positive  colloid  is 
added  to  the  solution  of  a  negative  colloid,  (1)  coagula- 
tion will  result,  and  (2)  the  coagulum  will  contain  both 
colloids,  for,  as  already  stated,  the  coagulum  obtained 
when  barium  chloride  is  added  to  arsenious  sulphide 
solution  contains  both  arsenious  sulphide  and  barium. 
The  experiments  carried  out  by  Biltz l  have  verified 
both  predictions.  This  investigator  showed,  first,  that  no 
coagulation  occurs  when  hydrosols  of  the  same  electrical 
sign  are  mixed.  When,  however,  a  solution  of  a  posi- 
tively charged  colloid  is  added  to  that  of  a  negatively 
charged  colloid  precipitation  occurs  in  all  cases,  unless 
the  quantity  of  the  added  colloid  is  relatively  either 
very  small  or  very  great.  For  a  certain  proportion 

1  Ber.  deut.  chem.  Ges.,  1904.  37,  1095. 


THE   SEPABATION  OF  COLLOIDS        209 

of  the  colloids  precipitation  of  both  is  complete ;  as  the 
quantities  deviate  from  this  optimal  ratio,  precipitation 
is  increasingly  incomplete.  It  is  possible,  for  instance,  to 
bring  about  the  complete  precipitation  of  arsenious 
sulphide  from  its  solution  by  the  addition  of  a  suitable 
quantity  of  ferric  hydroxide  hydrosol ;  similarly,  aniline 
blue,  which  forms  a  negative  hydrosol,  is  precipitated 
by  magdala  red,  which  forms  a  positive  hydrosol. 

The  precipitation  of  egg  albumin  by  solutions  of 
various  complex  acids — e.g.  molybdic,  tungstic,  and 
tannic  acids — furnishes  an  example  of  the  mutual  coagu- 
lation of  two  colloids.1  Metaphosphoric  acid,  too,  forms 
a  pseudo-solution  or  hydrosol  which  precipitates  albumin, 
while  the  crystalloidal  orthophosphoric  acid  has  no  such 
effect. 

An  interesting  case  in  which  the  reciprocal  coagulation 
of  two  colloids  has  been  employed  for  a  practical  purpose 
is  furnished  by  a  recent  investigation  of  Michaelis  and 
Eona.2  They  shew  that  mastic  suspension  and  a  faintly 
acid  solution  of  protein  precipitate  each  other  completely 
when  they  are  mixed  in  a  certain  proportion ;  if  they  are 
mixed  in  any  other  proportion,  the  precipitation  is  in- 
complete. This  observation  is  taken  as  the  basis  of 
a  method  for  the  removal  of  the  last  traces  of  proteins 
from  blood  serum.  The  bulk  of  the  protein  in  the  serum 
is  precipitated  with  alcohol,  and  the  filtrate,  containing 
not  more  than  1  per  cent,  of  protein  and  a  trace  of  acetic 
acid,  is  treated  with  excess  of  mastic  suspension.  This 
of  itself  does  not  bring  about  complete  precipitation  of 
the  protein,  but  if  the  excess  of  mastic  is  coagulated  by 
the  addition  of  a  small  quantity  of  an  electrolyte,  it 
carries  down  all  the  remaining  protein  with  it.  The 
filtered  liquid  is  then  free  from  both  mastic  and  protein. 

1  See  Mylius,  Ber.  deut.  chem.  Ges.,  1903,  36,  775 ;  Biltz,  loc.  cit. 
8  BMem.  Zeit.,  1907,  2,  219  ;  5,  365. 


210  PHYSICAL  CHEMISTRY 

The  Precipitation  of  Emulsoids. — Emulsoids  differ 
notably  from  suspensoids  in  their  slight  sensitiveness 
to  the  presence  of  neutral  alkali  salts.  Comparatively 
small  quantities  of  these  are  able  to  produce  coagulation 
of  arsenious  sulphide  or  ferric  hydroxide,  while  the 
quantities  required  to  cause  precipitation  of,  say,  serum 
albumin  from  its  solution  are  very  great.  The  precipita- 
tion of  an  emulsoid  by  a  neutral  alkali  salt  is  reversible, 
while  the  corresponding  precipitation  of  a  suspensoid 
is  irreversible.  Further,  the  factors  governing  the  pre- 
cipitation are  quite  different  in  the  two  cases.  All  the 
evidence  goes  to  show  that  the  precipitation  of  a  suspen- 
soid by  an  electrolyte  is  essentially  electrical  in  character; 
the  precipitation  of  a  reversible  colloid  by  a  neutral 
alkali  salt,  on  the  other  hand,  has  much  in  common  with 
the  phenomenon  of  '  salting  out,'  familiar  especially  to  the 
organic  chemist.  Electrical  influences  have  nothing  to 
do  with  the  precipitation  of  a  reversible  colloid,  for  as 
Pauli  has  shown,1  protein  from  serum  can  be  so  purified 
by  dialysis  that  even  in  a  steep  potential  gradient  it 
exhibits  110  tendency  to  migrate  either  towards  the  anode 
or  towards  the  cathode,  yet  in  this  neutral  condition  the 
protein  can  be  precipitated  by  alkali  salts;  hence  it 
is  clear  that  the  factors  which  determine  precipitation 
in  this  case  are  not  electrical. 

The  grounds  for  regarding  the  precipitation  of  emul- 
soids  by  neutral  alkali  salts  as  allied  to  the  pheno- 
menon of  '  salting  out '  rather  than  to  the  coagulation  of 
suspensoids  are  to  be  found  in  the  relative  effects  of 
these  salts.  The  results  of  many  investigations  of  the 
influence  of  salts  on  the  solubility  of  hydrogen,  carbon 
dioxide,  ethyl  acetate,  and  other  sparingly  soluble  sub- 
stances (compare  p.  26),  have  shown  that  the  effect  of 
any  particular  salt  is  the  sum  of  the  effects  of  the  ions ; 
1  Beitr.  chem.  PhysioL.  Path.,  1906,  7,  631. 


THE   SEPARATION   OF  COLLOIDS        211 

a  diminution  in  the  solubility  of  any  of  these  substances 
is  not  due  to  the  cation  in  one  case,  to  the  anion  in 
another,  as  in  the  coagulation  of  suspensoids ;  each  ion 
is  responsible  for  part  of  the  effect.  By  comparing  the 
effects  of  a  number  of  potassium  salts  in  lowering  the 
solubility  of,  say,  hydrogen  in  water,  it  is  possible  to 
arrange  the  anions  according  to  the  magnitude  of  their 
influence;  similarly,  by  comparing  the  effects  of  the 
chlorides  of  the  alkali  metals  on  the  solubility  of  hy- 
drogen, it  is  possible  to  arrange  the  cations  according 
to  the  magnitude  of  their  influence.  The  order  of  the 
anions  determined  in  this  way,  beginning  with  the  one 
which  is  most  effective  in  lowering  the  solubility  of 
hydrogen,  &c.,  is  SO/',  Cl',  Br',  I',  N03' ;  the  corresponding 
order  for  the  cations  is  Na",  K',  NH4*.  Hofmeister  and 
Pauli1  have  studied  in  a  similar  fashion  the  influence 
of  various  alkali  salts  in  precipitating  proteins,  and  they 
find  that  the  effect  of  a  given  alkali  salt  is  an  additive 
function  of  the  two  ions.  When  the  ions  are  arranged 
according  to  the  magnitude  of  their  effects,  the  following 
series  are  obtained,  the  first  member  of  each  series  being 
the  most  effective  in  causing  precipitation :  S04",  HP04", 
CH3.COO',  Cl',  NO/,  Br',  T,  CNS';  Li',  Na',  K',  NH4'. 
Comparison  of  these  with  the  previous  series  shows  that  the 
order  is  very  nearly  the  same  in  the  two  cases.  The 
precipitation  of  reversible  colloids  by  neutral  alkali  salts 
appears  therefore  to  be  closely  allied  to  the  process  of 
'  salting  out,'  and,  like  the  latter,  is  probably  connected 
with  the  hydration  of  the  salts.  This  result  emphasises 
the  fact  that  solutions  of  reversible  colloids  approximate 
more  to  true  solutions  that  do  solutions  of  suspensoids. 

When  a  neutral  solution  of  protein  is  made  slightly- 
acid  or  slightly  alkaline,  its  properties  undergo  a  marked 

1  See  Pauli,  Beitr.  chem.   Physiol.  Path.,   1902,   3,  225.      Compare 
Robertson,  J.  Biol.  Chem.,  1911,  9,  303. 


212  PHYSICAL   CHEMISTRY 

modification.  In  a  potential  gradient  the  protein  now 
migrates  towards  the  anode  or  cathode  according  as  the 
medium  is  alkaline  or  acid,  and  in  respect  also  to  the 
precipitating  power  of  salts  its  behaviour  now  resembles 
that  of  an  ordinary  suspensoid.1  The  properties  of  a 
protein  solution  containing  a  trace  of  alkali  or  acid  have 
accordingly  been  discussed  in  an  earlier  paragraph  of  this 
chapter,  where  it  was  shown  that  in  these  circumstances 
it  is  the  valency  of  the  cation  or  anion  which  is  the 
predominating  factor  in  determining  the  precipitation. 
The  modification  in  the  character  of  protein  which  results 
from  the  addition  of  small  quantities  of  acid  or  alkali  is 
demonstrated  also  by  its  behaviour  towards  salts  of  the 
heavy  metals.  These  are  unable  to  precipitate  carefully 
dialysed  neutral  protein,  but  as  soon  as  the  protein  has 
acquired  an  electro-negative  character,  it  is  readily  pre- 
cipitated by  small  quantities  of  these  salts ;  the  precipita- 
tion, further,  is  irreversible  in  character,  and  therefore 
quite  different  from  the  precipitation  of  neutral  protein 
by  alkali  salts. 

The  readiness  of  protein  to  change  its  character  with 
the  acid  or  alkaline  reaction  of  the  medium  becomes 
intelligible  on  the  basis  of  Hofmeister's  theory,  that  the 
proteins  are  produced  by  the  condensation  of  several 
amino  acids,  and  that  the  protein  molecule  is  character- 
ised by  the  presence  of  at  least  one  ainino  group  and 
one  carboxyl  group.  On  this  view  protein  is  an  '  am- 
photeric '  electrolyte,  that  is,  an  electrolyte  which  may  act 
either  as  an  acid  or  as  a  base — which  may  split  off  either 
hydrogen  or  hydroxyl  ions.  According  to  circumstances, 
therefore,  the  protein  molecule  may  assume  either  an  acid 
or  a  basic  function :  it  forms  salts  both  with  bases  and 
with  acids. 

1  Hardy,  Zeit.  physikal.  Chcm.,  1900,  33,  385  ;  also  Pauli,  Bcitr.  chem. 
Phytiol  Path.,  1906,  7,  531. 


THE   SEPAEATION  OF  COLLOIDS        213 

Protective  Action  of  Reversible  Colloids.— When  a 

reversible  colloid  is  added  to  the  solution  of  a  suspensoid, 
the  precipitation  of  the  latter  by  electrolytes  is  more  or 
less  inhibited.  This  is  not  generally  due  to  an  increase 
in  the  viscosity  of  the  medium,  and  consequently  increased 
resistance  to  sedimentation,  for  the  protective  effect  is 
produced  by  very  small  quantities  of  the  reversible  colloid, 
insufficient  to  cause  any  appreciable  change  of  viscosity. 
As  an  illustration  of  this  phenomenon  we  may  take  the 
influence  of  various  reversible  colloids  on  the  stability  of 
a  gum  mastic  suspension.  Bechhold  has  shown1  that 
while  a  mixture  of  1  cub.  cm.  mastic  suspension  f  1  cub. 
cm.  O'lN  MgS04  made  up  to  3  cub.  cm.  with  water 
is  completely  coagulated  in  15  minutes,  no  coagulation 
occurs  within  24  hours  if  2  drops  of  a  1  per  cent,  gelatin 
solution  are  added  before  making  up  to  3  cub.  cm. ;  the 
gelatin  '  protects  '  the  mastic.  The  coagulation  of  mastic 
suspension  is  similarly  inhibited  by  ox  blood  serum  and 
gum  arabic. 

An  extreme  case  of  this  protective  action  is  furnished 
by  the  colloidal  silver  halides  described  by  Paal  and  Voss.2 
These  are  obtained  by  adding  sodium  halide  to  silver 
hydroxide  in  presence  of  sodium  protalbate  or  lysalbate, 
salts  which  are  prepared  by  the  action  of  sodium  hydroxide 
on  egg  albumin.  The  colloidal  solutions  of  silver  halide 
so  obtained  are  opalescent,  and  yield  a  slightly  coloured 
solid,  containing  as  much  as  90  per  cent,  of  silver  halide, 
and  yet  dissolving  readily  in  cold  water.  It  is  probable 
that  in  such  cases  the  emulsoid  forms  a  thin  envelope 
round  each  suspensoid  particle,  and  so  prevents  the  aggre- 
gation and  consequent  flocculation  of  the  particles. 

Reversible  colloids  differ  appreciably  in  their  power  to 

1  Zeit.  pJiysikal.  Chem.,  1004,  48,  40b. 

2  Ber.  deut.  ckem.  Ges.,  1904,  37,  3862. 


214  PHYSICAL   CHEMISTRY 

protect  suspensoids  from  coagulation  by  electrolytes,  and 
an  attempt  has  been  made  by  Zsigmondy l  to  differentiate 
various  protein  substances  on  this  basis.  A  red  solution 
of  colloidal  gold  turns  blue  on  the  addition  of  sodium 
chloride  and  other  salts  owing  to  increase  in  size  of  the 
colloid  particles,  but  this  change  of  colour  may  be  pre- 
vented by  the  presence  of  proteins.  A  more  or  less 
definite  amount  of  each  protein  is  required  to  secure 
this  result,  and  the  proteins  may  be  classified  correspond- 
ingly. For  this  purpose  Zsigmondy  used  the  '  gold 
number,'  which  is  defined  as  the  weight  in  milligrams 
of  the  reversible  colloid  which  is  just  insufficient  to  pre- 
vent the  change  from  red  to  blue  in  10  cub.  cm.  of 
colloidal  gold  solution  after  the  addition  of  1  cub.  cm.  of 
10  per  cent,  sodium  chloride  solution.  How  far  the 
'  gold  number '  varies  from  one  case  to  another  will  be 
seen  from  the  following  table : — 

Gold  Number. 

Gelatin 0-005-  O'Ol 

Caseinogen O'Ol 

Globulin 0'02-0'05 

Egg  albumin  amorph 0-03-0-06 

Egg  albumin  cryst 2-8 

Fresh  egg-white 0-08-0-15 

It  is  noteworthy  that  albumoses  are  altogether  unable 
to  exert  a  protective  action  on  the  red  solution  of  colloidal 
gold. 

Colloids  in  Biology. — In  view  of  the  enormously  im- 
portant part  played  by  colloids  in  the  living  cell  itself 
and  in  all  physiological  fluids,  it  is  obvious  that  a  know- 
ledge of  the  peculiar  characteristics  of  these  substances 
is  a  necessary  preliminary  to  any  effort  to  interpret  vital 
phenomena.  In  recent  years  our  knowledge  of  the  pro- 

1  Zeit.  analyt.  Cliem.,  1901,  40,  697;  see  also  Schulz  and  Zsigmondy, 
Beitr.  chem.  Pltysiol.  Path.,  11)02,  3,  137. 


THE   SEPAEATION   OF   COLLOIDS         215 

perties  of  colloids  has  been  growing  rapidly,  and  numerous 
and  noteworthy  attempts  have  been  made  to  use  this  new 
knowledge  in  attacking  biological  problems  of  various 
kinds.  In  this  and  the  foregoing  chapters,  in  which  a 
brief  account  of  the  outstanding  characteristics  of  colloids 
has  been  given,  reference  has  been  made  incidentally  to 
various  cases  in  which  the  behaviour  of  colloids  seems  to 
have  a  direct  bearing  on  certain  biological  phenomena. 
There  are,  however,  numerous  other  problems  in  which 
colloids  are  essentially  involved,  and  on  which  much  new 
light  has  been  thrown  by  the  colloid  investigations  of  the 
past  ten  or  fifteen  years. 

In  this  period  much  work  has  been  done  with  the 
object  of  elucidating  the  nature  and  mode  of  action  of 
enzymes,  toxins,  and  antitoxins,  and  as  these  are  all  col- 
loids, it  is  only  natural  that  attempts  have  been  made  to 
correlate  their  behaviour  with  that  of  less  complex  bodies 
of  the  same  class.  As  a  first  example  of  such  correlation 
we  may  take  what  is  known  as  the  Danysz  phenomenon. 
The  toxicity  of  a  mixture  of  diphtheria  toxin  and  antitoxin 
depends  on  the  way  in  which  the  two  are  mixed.  If  the 
amount  of  toxin  added  is  such  that  the  mixture  is  non- 
toxic,  then  in  a  second  experiment,  in  which  the  same 
amounts  of  antitoxin  and  toxin  are  taken,  in  which, 
however,  the  toxin  is  added  in  instalments,  the  resulting 
mixture  is  toxic.  This  phenomenon  is  exactly  analogous 
to  what  happens  in  the  precipitation  of  a  colloid  by  an 
electrolyte,  or  in  the  precipitation  of  one  colloid  by  another; 
the  amount  of  electrolyte  or  colloid  required  for  complete 
precipitation  varies  according  as  it  is  added  all  at  once 
or  in  instalments.  The  condition  of  a  toxin-antitoxin 
mixture,  therefore,  resembles  that  of  colloidal  solutions 
in  that  it  is  not  completely  defined  by  a  statement  of 
its  composition;  its  character  depends  on  its  previous 
history. 


216  PHYSICAL   CHEMISTKY 

In  connection  also  with  the  agglutination  of  bacteria,1 
notable  attempts  have  been  made  to  interpret  some  at 
least  of  the  phenomena  by  reference  to  the  known  be- 
haviour of  ordinary  colloids.2  If  an  animal  is  inoculated 
with  cultures  of  typhoid  bacteria,  a  substance,  agglutinin, 
is  produced  in  the  serum,  and  this  substance,  when  added 
to  a  suspension  of  typhoid  bacteria,  causes  the  latter  to 
clump  together  and  to  sink  to  the  bottom  of  the  liquid 
in  which  they  are  suspended :  this  phenomenon  is  de- 
scribed as  '  agglutination.'  This  process  bears  a  general 
resemblance  to  the  precipitation  of  an  insoluble  salt  which 
frequently  follows  the  addition  of  one  salt  solution  to 
another,  but  to  conclude  from  this  that  the  interaction 
between  typhoid  bacteria  and  agglutiniu  is  purely  a 
chemical  reaction  would  be  unjustifiable.  For,  as  we 
have  seen,  a  colloid  may  be  precipitated  by  an  electrolyte 
or  by  another  colloid,  even  in  cases  where  the  possibility 
of  chemical  interaction  in  the  ordinary  sense  is  excluded. 

When  different  quantities  of  agglutinin  are  added 
to  a  given  quantity  of  typhoid  bacteria,  it  is  found 
that  for  one  particular  quantity  of  agglutinin  the  ag- 
glutination is  at  a  maximum.  If  either  a  very  small 
or  a  very  large  amount  of  agglutinin  is  added  to  the 
bacteria,  no  agglutination  whatever  occurs.  The  occur- 
rence of  such  maximum  effects  for  particular  concentra- 
tions of  the  interacting  substances  is  indeed  fairly  frequent 
in  the  field  of  immunity.  It  is  possible  to  regard  this 
phenomenon  as  the  analogue  of  what  happens  when 
sodium  hydroxide  is  gradually  added  to  a  solution  of 
alum ;  the  precipitate  first  formed  is  dissolved  by  excess  of 
the  reagent,  and  the  amount  of  precipitate  is  a  maximum 
for  certain  definite  proportions  of  alum  and  sodium 
hydroxide.  But  the  interaction  between  agglutinin  and 

1  Eisenberg  and  Volk,  Zeit.  Hygiene,  1302,  40,  155. 

2  Bechhold,  Zeit.  physikal.  Chem.,  1904,  48,  385  ;  Biltz,  ibid.,  615. 


THE   SEPARATION   OF  COLLOIDS        217 

bacteria  is  not  thereby  proved  to  be  purely  a  chemical 
effect,  for,  as  already  stated  (p.  209),  the  mutual  pre- 
cipitation of  colloids  is  characterised  by  the  same  features. 
When  one  of  the  colloids  is  in  very  large  excess  no 
precipitate  is  formed,  and  the  maximum  precipitation  for 
a  given  quantity  of  the  one  colloid  is  obtained  only  with 
a  certain  proportion  of  the  other  colloid. 

It  is  noteworthy  that  a  serum  containing  agglutinin 
can  agglutinate  bacteria  only  in  the  presence  of  the  salts 
of  the  serum;  if  the  serum  is  dialysed,  and  so  freed 
from  electrolytes,  no  agglutination  takes  place.  That  this 
should  be  so  is  not  surprising  when  we  bear  in  mind 
the  important  part  played  by  electrolytes  in  relation  to 
colloids.  A  suspension  of  agglutinin  bacteria — that  is, 
bacteria  which  have  been  treated  with  a  serum  containing 
agglutinin  and  thereafter  thoroughly  washed — resembles 
a  mastic  suspension  in  being  completely  precipitated  by 
small  quantities  of  salts,  and  Bechhold  (loc.  cit.)  has  shown 
that  the  precipitating  power  of  a  salt  in  relation  also  to 
agglutinin  bacteria  is  determined  mainly  by  the  valency 
of  the  cation.  A  suspension  of  typhoid  bacteria  alone, 
although  it  moves  towards  the  anode  in  a  potential 
gradient,  is  not  precipitated  by  sodium  chloride.  The 
bacteria  behave  like  suspended  particles  which  are  pro- 
vided with  a  coating  of  reversible  colloid,  and  are  so 
protected  from  the  action  of  salts  of  the  alkali  and  alkaline 
earth  metals. 

Such  are  a  few  of  the  cases  in  which  a  comparison 
of  the  agglutination  of  bacteria  and  the  properties  of 
ordinary  colloids  is  highly  suggestive.  The  problem  of 
agglutination,  however,  is  very  complex,  and  it  is  unlikely 
that  it  will  be  solved  merely  by  correlation  with  the 
phenomena  of  colloidal  solutions,  or  even  on  the  wider 
basis  of  an  adsorption  theory  (to  be  discussed  in  the 
following  chapter).  For  the  reaction  between  agglutinin 


218  PHYSICAL  CHEMISTRY 

and  bacteria  is  a  specific  one ;  typhoid  bacteria  are 
agglutinated  pre-eminently  by  the  serum  of  animals  pre- 
viously treated  with  cultures  of  typhoid  bacteria,  not  by 
the  serum  of  animals  inoculated  with  cultures  of  other 
bacteria.  Such  specific  characteristics  can  be  explained 
only  on  chemical  lines,  and  a  discussion  of  the  agglutina- 
tion of  bacteria  from  this  point  of  view  is  outside  the 
scope  of  the  present  volume. 

There  are  various  other  phenomena  of  physiological 
interest  in  which  the  mutual  precipitation  of  two  colloids 
is  a  main  feature,  and  in  the  interpretation  of  which  the 
conditions  governing  such  a  precipitation  must  be  borne 
in  mind.  There  is,  for  instance,  the  observation  that  if 
red  blood  corpuscles  from  one  animal  are  injected  into 
another  animal  of  a  different  species,  a  substance  is 
produced  in  the  serum  of  this  second  animal  which  has 
the  power  of  agglutinating  red  corpuscles  of  the  injected 
variety.  In  this  connection  it  is  worthy  of  mention  that 
when  blood  corpuscles  are  suspended  in  a  sucrose  solution, 
or  in  a  neutral  solution  of  an  alkali  or  alkaline  earth 
salt,  they  move  towards  the  anode  in  a  potential  gradient. 
Hober l  attributes  this  to  the  protein  and  lecithin  present 
in  the  plasmatic  membrane ;  these  substances  generally 
exhibit  anodic  convection.  Like  these  also,  the  blood  cor- 
puscles reverse  their  migration  when  a  little  acid,  copper, 
silver,  iron,  or  aluminium  salt  is  added  to  the  medium 
in  which  they  are  suspended.  A  suspension  of  red  blood 
corpuscles  is  agglutinated  not  only  by  serum  obtained 
from  an  animal  which  has  been  inoculated  with  these 
corpuscles,  but  also  by  numerous  colloids,  positive  as  well 
as  negative — stannic  acid,  ferric  hydroxide,  mastic,  and 
various  dyes. 

1  Pfliiger's  Arch.,  1904,  101,  607 ;  102,  196. 


CHAPTER   XI 

ADSORPTION 

Surface  Development  in  Colloids.  —  It  is  not  pro- 
posed to  discuss  in  detail  in  this  volume  the  various 
theories  which  have  been  brought  forward  dealing  with 
the  stability  of  colloidal  solutions  and  with  the  separa- 
tion of  colloids  from  their  solutions.1  Two  factors, 
however,  which  must  obviously  enter  into  any  inter- 
pretation of  the  relation  between  a  colloid  and  its 
medium  may  be  noted  here.  There  is,  firstly,  the 
existence  in  a  great  many  cases  at  least  of  a  potential 
difference  between  the  colloid  particles  and  the  surround- 
ing medium,  and  secondly,  the  relatively  enormous  surface 
of  contact  between  the  colloid  and  its  environment.  The 
importance  of  the  electrical  factor  will  have  become  plain 
to  the  reader  from  the  facts  described  in  the  two  pre- 
ceding chapters.  A  little  consideration  will  show  that 
the  other  factor,  which  we  may  call  the  surface  factor, 
is  equally  important  in  the  interpretation  of  the  pheno- 
mena exhibited  by  colloids.  All  the  facts  go  to  show 
that  a  colloidal  solution  is  essentially  non-homogeneous; 
it  is  what  is  known  as  a  two-phase  system,  built  up 
of  a  fluid  medium  containing  definite  and  distinct  sus- 
pended particles  in  an  extreme  state  of  subdivision. 
With  the  help  of  the  ultramicroscope  it  is  possible  in 

1  See,  for  instance,  Hardy, Zeit.  physilcal.  Chem.,  1900,  33,  385;  Bredig, 
Anorgan.  Fermente,  Leipzig,  1901  ;  Billitzer,  Zeit,  physilcal.  Chem.,  1904, 
45,  327 ;  1905,  51, 129  ;  Michaelis,in  Koranyi  and  Kichter's  Physikalischc 

Chemie  und  Mcdizin,  Leipzig,  1908. 

219 


220  PHYSICAL  CHEMISTRY 

a  great  many  cases  to  detect  these  particles  and  to 
follow  their  movements.  Now,  when  a  given  quantity 
of  matter  is  divided  up  more  and  more  finely,  its  sur- 
face area  is  immensely  increased.  Suppose,  for  instance, 
that  a  compact  sphere  of  any  material  with  a  diameter 
of  1  mm.,  and  therefore  a  surface  area  of  0-0314  sq. 
cm.,  were  divided  up  into  a  number  of  small  spheres 
each  with  a  diameter  of  O'Ol  mm.  The  number  of 
spheres  would  now  be  106,  and  the  total  area  of  their 
surfaces  would  be  3 '14  sq.  cm.  If  the  division  were 
carried  farther  until  each  small  sphere  had  a  diameter 
of  O'OOOl  mm.,  and  would  therefore  be  hardly  visible 
under  the  microscope,  their  number  would  be  1012,  and 
the  total  area  of  their  surfaces  would  be  314  sq.  cm. 
To  bring  about  such  a  subdivision  requires  the  application 
of  energy,  which  is  stored  up  in  the  finely  divided  spheres 
in  the  form  of  surface  energy ;  this  is  defined  as 
the  product  -  surface  area  x  surface  tension.  In  two- 
phase  systems,  therefore,  where  the  surface  of  the  one 
phase  is  developed  to  a  relatively  high  degree,  as  it  is 
in  colloidal  solutions,  the  surface  energy  becomes  an 
important  factor  in  determining  the  behaviour  of  the 
system.1  Especially  is  this  the  case  where  a  change 
in  the  aggregation  of  colloid  particles  is  concerned; 
this  means  a  change  in  the  surface  area,  and  this  again 
involves  a  change  of  the  surface  energy. 

It  has  been  stated  above  that  in  the  relationship 
between  a  colloid  and  its  environment  electrical  energy 
also  is  involved.  The  parts  played  by  electrical  and 
surface  energy  respectively  in  the  phenomena  of  colloidal 
solutions  are  not  however  independent  of  each  other : 
there  is  a  close  connection  between  the  two.  It  is 

1  It  is  an  interesting  question  whether  this  argument,  cannot  be 
extended  to  cover  the  case  of  cry stalloidal  solutions,  regarded  as  two- 
phase  systems.  See  Wo.  Ostwald,  Grundriss  der  Kolloidchemie,  p.  126. 


ADSORPTION  221 

well  known  that  the  surface  tension  of  mercury  in  con- 
tact with  a  sulphuric  acid  solution  is  affected  by  altera- 
tions in  the  potential  difference  between  metal  and 
solution.  Obviously,  in  view  of  the  fact  that  electrical 
charges  of  the  same  sign  repel  each  other,  the  existence 
of  a  charge  at  the  surface  of  the  mercury  tends  to  increase 
the  surface,  and  is  therefore  opposed  to  the  surface  tension, 
which  tends  to  diminish  the  surface.  A  reduction  in  the 
electrical  charge  at  the  surface  means  an  increase  in  the 
surface  tension.  This  example  shows  that  in  the  case  of 
colloidal  solutions  the  connection  between  the  electrical 
and  surface  factors  must  be  very  close. 

Instead  of  following  out  the  influence  of  these  factors 
in  determining  the  properties  of  colloids,  as  has  been 
attempted  by  Hardy,  Bredig,  Billitzer,  and  others,  we 
shall  consider  the  phenomena  exhibited  by  colloids  from 
a  wider  point  of  view  which  has  been  very  generally 
adopted  in  recent  years.  We  may  regard  the  interaction 
of  colloids  with  each  other  and  with  various  solid  and 
dissolved  substances  as  being  essentially  a  process  of 
'  adsorption.'  This  term  is  used  to  describe  a  phenomenon 
which  is  frequently  observed  when  a  foreign  substance 
is  introduced  into  a  two-phase  system.  When  opportunity 
is  afforded  this  foreign  substance  to  distribute  itself 
throughout  the  system,  it  is  often  found  to  be  locally 
concentrated  at  the  surface  of  one  of  the  phases.  This 
concentration,  as  will  appear  from  the  cases  discussed 
below,  is  not  generally  to  be  regarded  as  a  chemical  process ; 
the  phenomenon  is  physical  in  character,  and  is  especially 
striking  when  the  surface  of  the  adsorbing  phase  is  highly 
developed.  It  is  in  regard  to  this  local  concentration 
011  the  surface  that  adsorption  differs  from  absorption ; 
when  we  speak  of  a  gas  as  being  absorbed  by  a  liquid, 
we  picture  the  gas  as  distributed  uniformly  throughout 
the  mass  of  the  liquid.  Perhaps,  however,  we  can  best 


222  PHYSICAL   CHEMISTRY 

appreciate  what  is  involved  in  the  term  '  adsorption ' 
by  studying,  first,  the  distribution  of  a  substance  in  a 
two-phase  system  where  no  surface  concentration  occurs. 

Distribution  of  a  Substance  between  Two  Immiscible 
Liquids. — When  a  substance  is  shaken  up  with  two  immis- 
cible liquids,  some  of  it  is  found  to  be  dissolved  in  the  one 
layer,  some  of  it  in  the  other  layer ;  it  is  said  to  be  '  dis- 
tributed '  between  the  two  phases.  The  absolute  amount 
of  the  substance  found  in  each  liquid  layer  after  equilibrium 
has  been  established  will  naturally  depend  on  the  volume 
of  each  liquid  taken,  but  if  we  eliminate  this  by  comparing 
the  concentrations  (i.e.  weights  per  unit  volume)  of  the 
substance  in  the  two  layers,  we  get  a  definite  measure 
of  the  distribution.  If  cl  is  the  concentration  of  the 
substance  in  the  first  liquid,  and  c2  its  concentration  in 

the   second    liquid,  then    the   ratio   ^   is   known   as   the 

ci 

'partition  coefficient'  or  the  'distribution  ratio.'  Ex- 
periment has  shown  that  if  the  molecular  condition 
of  the  dissolved  substance  is  the  same  in  each  of  the 
two  liquids,  then  the  partition  coefficient  is  independent 
of  the  absolute  values  of  cl  and  c2,  independent,  in  other 
words,  of  the  concentration.  This  is  illustrated  by  the 
figures  in  the  following  table  relating  to  the  distribution 
of  iodine  between  water  and  carbon  tetrachloride ; l 
the  figures  in  the  first  column  (cx)  are  the  concentrations 
of  iodine  in  the  aqueous  layers,  those  in  the  second 
column  are  the  concentrations  of  iodine  in  the  corre- 
sponding carbon  tetrachloride  layers : — 


0-2913 

25-61 

ci 
87-9 

0*1934 

16-54 

85-5 

0*1276 

10-88 

85-3 

0-0818 

6-966 

85-1 

0-0516 

4-412 

85-8 

1  Jakowkin,  Zeit.  physikal.  Chem,,  1895,  18,  585, 


ADSORPTION  225 

The  rule,  of  which  the  foregoing  figures  are  an 
illustration,  namely,  that  the  ratio  of  the  concentrations 
of  a  substance  distributed  in  two  immiscible  liquids  is 
independent  of  the  concentration,  is  really  the  same 
as  Henry's  law  dealing  with  the  absorption  of  a  gas 
by  a  liquid  under  varying  pressures.  In  an  earlier 
part  of  this  volume  (p.  20)  it  was  stated  that  accord- 
ing to  Henry's  law  the  quantity  of  gas  dissolved  by  a 
given  quantity  of  a  liquid  at  a  given  temperature  is 
proportional  to  the  pressure.  Suppose  that  a  given 
quantity  of  water  is  shaken  up  with  hydrogen  (1)  at 
1  atmosphere  pressure,  (2)  at  3  atmospheres  pressure, 
until  saturation  is  complete  in  each  case,  that  is, 
until  equilibrium  is  established  between  the  gas  phase 
and  the  liquid  phase.  According  to  Henry's  law,  the 
quantity  of  gas  dissolved  in  the  liquid  in  the  second 
case  is  three  times  as  great  as  it  is  in  the  first  case, 
that  is,  its  concentration  in  the  liquid  phase  is  three 
times  as  great.  But  the  hydrogen  in  the  second  case 
is  under  3  atmospheres  pressure  as  compared  with 
1  atmosphere  in  the  first  case,  and  the  concentration 
in  the  gas  phase  will  have  increased  in  the  same  pro- 
portion. The  ratio,  therefore,  of  the  concentrations 
of  hydrogen  in  the  gas  phase  and  in  the  water  is  the 
same  under  3  atmospheres  as  under  1  atmosphere ; 
or,  putting  it  generally,  the  ratio  of  the  concentrations 
of  the  gas  in  the  gas  phase  and  in  the  liquid  phase, 
when  equilibrium  has  been  established,  is  independent 
of  the  pressure.  Expressed  in  this  form,  Henry's  law 
is  seen  to  be  practically  identical  with  the  rule  relating 
to  the  distribution  of  a  substance  between  two  immiscible 
liquids. 

Such  a  distribution  is  a  physical  process ;  it  can  be 
regarded  as  chemical  only  in  so  far  as  we  regard  the 
process  of  solution  of,  say,  sucrose  in  water  as  due  to 

p 


224  PHYSICAL   CHEMISTRY 

the  action  of  chemical  forces.  It  ought  to  be  noted 
also  that  when  a  gas  is  dissolved  in  a  liquid,  or  when  a 
substance  is  distributed  between  two  immiscible  liquids, 
the  equilibrium  which  is  established  is  reversible,  that 
is,  it  -can  be  reached  from  both  sides.  Suppose,  for 
instance,  that  100  cub.  cm.  of  water  are  shaken  with 
20  cub.  cm.  of  a  solution  of  iodine  in  carbon  tetrachloride  ; 
equilibrium  is  rapidly  established,  when  it  will  be  found 
that  some  of  the  iodine  has  gone  into  the  water.  Suppose 
that,  in  a  second  experiment,  100  cub.  cm.  of  water  are 
shaken  with  10  cub.  cm.  of  an  iodine  solution  of  double 
the  concentration  of  the  first  one.  When  equilibrium 
is  reached  the  100  cub.  cm.  of  water  will  be  found  to 
contain  more  iodine  than  in  the  first  case.  If,  however, 
another  10  cub.  cm.  of  carbon  tetrachloride  are  added 
and  the  mixture  is  shaken,  the  extra  iodine  is  taken 
out  of  the  water,  and  the  equilibrium  finally  reached  is 
the  same  as  in  the  first  case. 

If  the  molecular  condition  of  the  dissolved  substance 
is  different  in  the  two  liquids,   then  the  value  of  the 

ratio  —  is  not  independent  of  the  concentration.     This 

ci 
statement  is  borne  out  by  the  following  figures  relating 

to  the  partition  of  acetic  acid  between  benzene  and 
water:1  —  q  is  the  concentration  of  the  acid  in  the 
benzene  layer,  c2  the  concentration  in  the  aqueous  layer. 


0-043  0-245  5-7  1-40 

OO71  0-314  4-4  1-39 

0-094  0-375  4-0  1'49 

0-149  0-500  3-4  1'67 

It  is  obvious  that  the  partition  coefficient   varies  with 

the  concentration,  and  this  is  to  be  attributed  to  the  fact 

1  Nernst,  Zeit.  physikal.  Chem.,  1891,  8,  110. 


ADSORPTION  225 

that  the  molecular  condition  of  acetic  acid  is  not  the 
same  in  benzene  as  it  is  in  water.  From  the  depression 
of  the  freezing  point  produced  by  acetic  acid  in  these 
two  solvents,  it  is  known  that  the  acid  in  benzene 
solution  consists  almost  entirely  of  double  molecules 
(although  the  proportion  of  simple  molecules  increases 
with  dilution),  whereas  acetic  acid  in  water,  apart  from 
the  slight  electrolytic  dissociation,  exists  in  the  form 
of  simple  molecules.  Now,  on  theoretical  grounds  it 
follows  that  if  the  molecular  weight  of  the  dissolved 
substance  in  the  first  liquid  is  n  times  the  molecular 

weight   in   the   second   liquid,   then   the   ratio  -JL  ought 

ci 

to  have  a  constant  value  independent  of  the  concen- 
tration. From  what  has  been  said,  it  is  evident  that 
for  the  partition  of  acetic  acid  between  benzene  and 
water  n  =  2,  and  we  should  therefore  expect  the  value  of 

-2 

_?.  to   be   independent   of   the   concentration.1      This    is 

ci 

approximately    the   case,    as    shown   by   the    figures   in 

the  last  column  of  the  foregoing  table,  and  such  varia- 
tion as  the  figures  show  is  probably  due  to  the  fact 
that  the  proportion  of  simple  molecules  in  a  benzene 
solution  of  acetic  acid  increases  somewhat  on  dilution. 

If,  conversely,  the  distribution  of  a  substance  between 
two   liquids   at   various   concentrations   has   been   found 

to  be  such  that  ?*    is  independent  of  the  concentration, 

ci 

the  conclusion  may  be  drawn  that  the  molecular  weight 
of  the  substance  in  the  first  liquid  is  n  times  that  in 
the  second  liquid. 

Equilibrium  between  a   Gas   and  a   Solid. — As  an 

example  of   a  case   where   surface   effects   become   pro- 
minent, we    may   take,  first,  the   distribution  of   a    gas 
1  Nernst,  loe.  cit. 


226  PHYSICAL   CHEMISTRY 

between  a  gas  phase  and  a  solid  phase ;  that  is,  we 
shall  consider  the  way  in  which  the  amount  of  a  gas 
taken  up  by  a  solid  varies  with  the  pressure  of  the 
gas.  In  view  of  the  results  obtained  in  connection 
with  the  distribution  of  a  substance  between  two  non- 
miscible  liquids,  it  might  be  expected  that  a  study  of 
the  equilibrium'  between  a  gas  and  a  solid  would  lead 
to  a  knowledge  of  the  molecular  condition  of  the  gas 
which  is  taken  up  by  the  solid.  This  expectation, 
however,  is  not  fulfilled,  for  the  taking  up  of  a  gas 
by  a  solid  is  found  to  be  determined  mainly  by  surface 
effects. 

The  facts  can  best  be  explained  by  reference  to  the 
case  of  carbon  dioxide  and  carbon,  studied  by  Travers.1 
This  investigator  determined  the  concentration  (x)  of 
carbon  dioxide  in  the  carbon  at  various  pressures  (P), 
sufficient  time  of  course  being  allowed  for  the  gas  and 
solid  to  come  into  equilibrium  with  each  other.  The 
results  obtained  at  0°  C.  are  recorded  in  the  first  two 
columns  of  the  following  table : — 

x 
P  mm.  x.  sTp  • 

4-1  0-38  0-24 

25-1  0-77  0-26 

137-4  1-45  0-26 

416-4  2-02  0-27 

858-6  2-48  0'26 

From  a  consideration  of  these  it  is  seen  that  the  amount 
of  carbon  dioxide  taken '  up  by  the  carbon  increases 
much  more  slowly  than  the  pressure.  Travers  found, 
however,  that  x  increases  proportionally  to  the  cube  root 
of  P,  as  is  shown  by  the  constancy  of  the  figures  in  the 
third  column  of  the  table,  and  the  question  arises :  What 
interpretation  is  to  be  given  of  this  relationship  between 

Proc.  Roy.  Soc.,  A,  1906,  78,  9.     Compare  Homfray,  ibid.,  1910, 
84,  99. 


ADSORPTION  227 

P  and  xf  How  is  it  that  a  similar  relationship,  ex- 
pressed by  the  equation  ^p  =  const,  is  found  for  carbon 

dioxide  and  carbon  at  other  temperatures,  as  well  as 
for  hydrogen  and  carbon?  If  we  suppose  that  the 
gas  is  uniformly  distributed  throughout  the  carbon, 
forming  a  solid  solution,  and  reason  by  analogy  from 
Nernst's  experiments  on  the  partition  of  acetic  acid 
between  water  and  benzene,  we  should  reach  the  con- 
clusion that  the  molecular  weight  of  carbon  dioxide  in 
carbon  is  one-third  of  its  molecular  weight  in  the  gaseous 
condition.  It  is  obvious  that  on  chemical  grounds  this 
conclusion  must  be  rejected,  and  it  appears  therefore 
that  to  regard  the  carbon  dioxide  as  uniformly  dis- 
tributed through  the  carbon,  and  so  forming  a  homo- 
geneous solid  solution,  is  not  permissible.  There  are 
various  indications,  in  this  and  similar  cases,  that  the 
surface  of  the  solid  is  mainly,  if  not  exclusively,  con- 
cerned in  taking  up  the  gas,  and  the  phenomenon  is 
accordingly  described  as  'adsorption'  rather  than  'ab- 
sorption/ 

Adsorption  by  a  Solid  from  a  Solution. — Very 
similar  to  the  phenomena  just  discussed  is  the  power 
of  carbon  to  adsorb  various  substances  from  their 
solutions.  Numerous  cases  of  this  adsorption  have 
recently  been  investigated  with  the  object  of  discovering 
the  nature  of  the  equilibrium  between  the  carbon  and 
the  solution,  and  of  finding  how  the  quantity  of  sub- 
stance adsorbed  by  the  carbon  varies  with  its  concen- 
tration in  the  solution. 

It  is  noteworthy  that  the  adsorption  equilibria  between 

carbon  and  an  aqueous  solution  are  reversible — that  is, 

they  can  be  reached  from  either  side.     An  illustration 

of  this  important  point  may  be  quoted.1     One  gram  of 

1  Freundlich,  Zeit.  physikal.  Chem.,  1906,  57,  385. 


228  PHYSICAL  CHEMISTRY 

carbon  was  shaken  for  20*5  hours  with  100  cub.  cm. 
of  a  O'OGSSN  solution  of  acetic  acid;  by  this  time 
equilibrium  was  established,  and  it  was  found  that  the 
acid  solution  was  now  0-0608N.  In  another  experiment 
one  gram  of  the  same  carbon  was  shaken  for  21  hours 
with  50  cub.  cm.  of  a  01376N(  =  0-Q688  x  2)  solution 
of  acetic  acid;  50  cub.  cm.  of  water  were  then  added, 
and  the  mixture  was  shaken  for  an  hour,  at  the  end 
of  which  time  it  was  found  that  the  acid  solution  was 
0'0606N.  This  is  practically  the  same  value  as  in 
the  first  case,  which  shows  that  the  same  equilibrium 
is  reached  when  the  carbon  is  charged  directly  with 
the  acid  as  when  a  slightly  overcharged  carbon  is 
deprived  of  part  of  its  adsorbed  acid. 

In  the  experiments  which  have  just  been  described 
the  carbon  was  shaken  with  the  acid  for  about  20  hours 
in  order  to  secure  the  establishment  of  equilibrium. 
In  reality,  however,  the  time  required  is  remarkably 
short.  It  has  been  found  that  when  a  solution  of 
acetic  acid  is  added  to  carbon,  once  shaken  with  the 
hand,  and  then  allowed  to  stand  for  20  minutes,  the 
concentration  of  the  solution  has  fallen  very  nearly 
to  its  equilibrium  value.  This  observation  supports  the 
view  that  the  taking  up  of  acetic  acid  from  its  solutions 
by  carbon  is  a  process  in  which  the  surface  of  the 
carbon  is  mainly  concerned,  for  the  penetration  or 
diffusion  of  the  acid  into  the  interior  of  the  carbon 
granules  could  only  be  a  comparatively  slow  process. 

The  relation  between  the  concentration  of  acetic  acid 
in  the  carbon  and  that  in  the  solution  when  equilibrium 
has  been  reached  is  brought  out  by  the  figures  in  the 
following  table.1  Those  in  the  first  column  (ct)  repre- 
sent the  equilibrium  concentrations  of  the  acetic  acid 

1  Freundlich,  loc.  cit. 


ADSOKPTION  229 

in  the  solutions,  and  are  given  in  millimolecules  per 
cub.  cm.  ;  the  figures  in  the  second  column  (cs  observed) 
represent  the  equilibrium  concentrations  of  the  acetic 
acid  in  the  carbon,  and  are  given  in  millimolecules 
per  1  gram  of  carbon.  A  glance  at  the  table  shows 
that  the  amount  of  acetic  acid  taken  up  by  the  carbon 
increases  much  more  slowly  than  its  concentration  in 
the  solution.  In  this  respect  the  adsorption  of  dissolved 
acetic  acid  by  carbon  and  the  adsorption  of  carbon 
dioxide  by  the  same  substance  are  closely  similar. 


Adsorption  of  Acetic  Acid  by  Carbon. 

/3  =  2'606.                              p  =  2'3 

ct. 

c,  observed. 

c,  calculated. 

0-0181 

0-467 

0-474 

0-0309 

0-624 

0-596 

0-0616 

0-801 

0-798 

0-1259 

I'll 

1-08 

0-2677 

1-55 

1-49 

0-4711 

2-04 

1-89 

0-8817 

2-48 

2-47 

2-785 

3-76 

4-01 

The  parallelism,  however,  goes  further,  for  the  relation- 
ship between  the  concentrations  of  acetic  acid  in  the  solu- 
tion and  in  the  carbon  can  be  represented  by  a  formula 


of  the  same  general  type  as   i^p  =  const.     This    general 

\_ 
adsorption  formula  is  cs  =  /3  .  c?  ,  in  which  /3  and  p  are 

constants  for  a  given  temperature  and  a  given  dissolved 
substance,  while  c,  and  ct  represent,  as  already  stated, 
the  concentration  of  the  dissolved  substance  in  the  solid 
and  liquid  phase  respectively.1  The  applicability  of  this 

formula  to  the  adsorption  of  acetic  acid  by  carbon  may  be 

i^ 
tested  by  assuming  that  the  formula  c3—{$.  ctp  is  valid  in 

this  case,  and  then  using  the  experimental  figures  of  the 
first  two  columns  to  evaluate  /3  and  p.  The  mean  values  so 

'l  For  other  formulae  see  Arrhenius,  Medd.   K.   Vetensk.  Nobelinst., 
1911,  2,  No.  7,1. 


230  PHYSICAL   CHEMISTRY 

obtained  are  (3  =  2*606  and  ^?  =  2*35.  ""When  these  figures 

are  put  in  the  general  formula,  we  get  cs  =  2'606o^ ,  so  that 
from  the  ascertained  value  of  clt  given  in  the  first  column, 
we  can  calculate  what  the  value  of  cs  ought  to  be.  Agree- 
ment between  the  value  of  ct  so  calculated  and  the  ex- 
perimental value  of  cs  furnishes  a  proof  of  the  applicability 
of  the  original  exponential  formula.  The  numbers  in  the 
third  column  of  the  foregoing  table  are  the  calculated 
values  of  cs  for  each  solution,  and  it  will  be  seen  that 

they  agree  remarkably  well  with  the  observed  values. 

i 

The  empirical  exponential  formula,  then,  cs  =  @.cv> 
may  be  taken  as  representing  the  adsorption  equilibrium 
between  carbon  and  aqueous  acetic  acid.  Freundlich  has 
further  shown  that  the  same  general  formula  is  applicable 
to  the  adsorption  of  many  other  substances  by  carbon, 
not  only  from  their  aqueous  solutions,  but  also  from  their 
solutions  in  alcohol,  benzene,  and  ether.  The  value  of  p 
varies  from  one  case  to  another,  but  only  within  somewhat 
narrow  limits ;  it  appears,  therefore,  to  be  to  a  large  extent 
independent  of  the  solvent  and  the  dissolved  substance. 
Thus  for  benzoic  acid  in  water  p  —  2*96  ;  bromine  in  water, 
p  =  344;  picric  acid  in  water,  _p  =  4'l7 ;  benzoic  acid  in 
ether,  ^>  =  2'2.  The  similarity  between  the  adsorption 
of  two  such  different  substances  as  benzoic  acid  and 
bromine,  evidenced  by  the  comparatively  slight  difference 
in  the  values  of  -p,  is  particularly  striking,1  and  may 
be  taken  as  showing  that  the  process  of  adsorption  is 
not  generally  a  chemical  phenomenon  in  the  ordinary 
sense,  as  has  been  maintained  in  some  quarters. 

Further,  when  a  solution  of  a  substance  is  shaken  up 
with  a  solid  with  which  it  may  react  chemically,  the 
equilibrium  reached  'is  essentially  different  from  the 

1  See  Freundlich,  Zcit.  Chem.  IndtJZoll.,  1908,  3,  212, 


ADSORPTION  231 

adsorption  equilibrium  between,  say,  carbon  and  aqueous 
acetic  acid.  The  difference  is  well  brought  out  in  an 
investigation  by  Walker  and  Appleyard1  of  the  equili- 
brium between  solid  diphenylamine  and  an  aqueous 
solution  of  picric  acid.  Diphenylamine  unites  with 
picric  acid  to  form  a  compound,  diphenylammonium 
picrate,  and  both  the  amine  itself  and  the  compound 
are  practically  insoluble  in  water.  The  compound  is 
capable  of  dissociating  into  its  constituents,  for  when 
it  is  treated  with  water  some  of  the  picric  acid  dissolves, 
and  an  equivalent  quantity  of  diphenylamine  remains 
behind ;  if  the  treatment  with  water  is  continued  long 
enough,  all  the  picric  acid  is  extracted  from  the  com- 
pound. In  their  experiments  Walker  and  Appleyard  shook 
three  lots  of  50  cub.  cm.  of  saturated  picric  acid  solution 
(  =  16-8  mg.  acid  per  gram  of  water  at  4O6°)  with  2 
grams,  1  gram,  and  O5  gram  of  diphenylamine  for  4J 
hours,  and  then,  equilibrium  having  been  reached, 
determined  the  concentrations  of  the  picric  acid  in  the 
water  and  in  the  diphenylamine.  The  results  for  the 
three  experiments  are  shown  in  the  adjoining  table : — 

Milligrams  of  Picric  Acid. 
In  1  gram  Water.  In  1  gram  Diphenylamine. 

13-8  7-5 

137  15-5 

13-8  30-0 

It  is  obvious  that  the  equilibrium  concentration  of  the 
picric  acid  in  the  diphenylamine  has  risen  steadily, 
while  that  in  the  solution  has  remained  constant. 

These  results  are  quite  distinct  from  the  adsorption 
phenomena  already  discussed,  and  show  how  the  distri- 
bution of  a  substance  between  a  liquid  and  a  solid 
phase  is  affected  by  the  intervention  of  chemical  affinity. 
This  is  an  important  point,  and  it  may  be  well  to 
1  Journ.  Chem.  Soc.,  1806,  69,  1334. 


232 


PHYSICAL   CHEMISTRY 


indicate  graphically  the  distinction  between  adsorption 
and  chemical  combination ;  this  may  be  done  by  tracing 
in  each  case  the  curve  which  represents  the  corre- 
sponding variations  of  ca  and  ct.  Suppose,  in  the  first 
place,  that  we  have  a  case  of  pure  adsorption,  to  which 
the  exponential  formula  is  applicable.  Such  a  case  is 
represented  by  the  continuous  curve  1,  which  is  concave 
to  the  ct  axis.  Its  course  is  obviously  in  harmony  with 
the  observation  which  is  made  in  all  cases  of  adsorp- 
tion, namely,  that  cs  increases  much  more  slowly  than 


FIG.  23. 

d ;  for  very  small  values  of  ct  the  adsorption  is  relatively 
complete.  In  a  case  of  chemical  combination,  on  the 
other  hand,  none  of  the  dissolved  substance  is  taken 
up  by  the  solid  until  its  concentration  in  the  solution 
reaches  a  certain  value  (13 '8  mg.  picric  acid  per  gram 
of  water  in  the  case  studied  by  Walker  and  Appleyard) ; 
up  to  this  point,  that  is,  GI  increases  steadily,  while 
cs  remains  equal  to  zero.  When  the  critical  value  is 
reached,  however,  any  attempt  to  increase  c,  further 
results  merely  in  an  increase  of  cs,  while  ct  remains 
constant.  This  continues  until  the  formation  of  the 


ADSORPTION  233 

compound  is  complete,  when  ct  may  increase  again.  The 
curve  2,  therefore,  representing  the  variation  of  cs  and 
ct  in  the  case  where  the  solid  forms  a  compound  with 
the  dissolved  substance,  is  simply  a  broken  line,  the 
vertical  part  of  which  corresponds  with  the  interval 
over  which  formation  of  the  compound  is  proceeding. 

In  view  of  the  distinction  which  has  just  been  drawn, 
it  is  fairly  clear  that  the  fixation  of,  say,  acetic  acid 
by  carbon  is  not  due  to  any  chemical  interaction  in 
the  ordinary  sense.  The  suggestion  that  acetic  acid 
forms  a  solid  solution  in  carbon  must  also  be  rejected, 
for  in  this  case  we  should  have  to  conclude  from  the 
observed  recorded  data  that  the  molecular  weight  of 
acetic  acid  dissolved  in  carbon  is  less  than  half  its 
molecular  weight  in  water.  This  is  not  in  the  least 
credible.  At  the  same  time  it  must  be  allowed  that 
in  certain  other  cases  there  is  evidence  for  the  formation 
of  a  solid  solution  in  addition  to  surface  adsorption. 
Thus  Davis  has  shown,1  in  a  study  of  the  equilibrium 
between  carbon  and  a  solution  of  iodine  in  various 
organic  solvents,  that  when  the  carbon  is  brought  into 
contact  with  an  iodine  solution  there  is,  first,  a  surface 
condensation,  which  is  complete  in  a  few  hours,  followed 
by  a  slow  diffusion  into  the  mass  of  the  carbon;  this 
latter  process  goes  on  for  weeks  or  months.  In  ex- 
periments carried  on  for  only  a  short  time,  the  same 
equilibrium  point  is  reached  from  both  sides,  but  the 
amount  of  iodine  contained  in  the  carbon  under  such 
equilibrium  conditions  is  much  less  than  the  amount 
which  it  takes  up  after  prolonged  contact  with  the 
iodine  solution. 

In  the  cases  of  adsorption  which  have  been  cited  so 
far,  there  can  be  no  doubt  that  surface  condensation 

1  Journ.  Chem.  Soc.,  1907,  91,  1666.  See  also  McBain,  Zeit.  physikal. 
Chem.,  1909,  68,  471. 


234  PHYSICAL  CHEMISTRY 

plays  the  main  part,  and  indeed  it  appears  that  on 
thermodynarnical  grounds  the  most  stable  condition  of 
any  solution,  when  surface  tension  considerations  only 
are  taken  into  account,  is  the  one  characterised  by  a 
minimum  surface  tension.  Hence  if  the  solute  lowers 
the  surface  tension  of  the  solvent,  it  will  accumulate 
in  the  surface  layer  of  the  solution.  Such  spontaneous 
accumulations  in  surface  layers  are  well  known.  Rams- 
den  has  shown1  that  solid  or  highly  viscous  coatings  are 
formed  on  the  free  surfaces  of  protein  solutions,  of  other 
colloidal  solutions,  of  fine  and  coarse  suspensions,  and  of 
a  few  apparently  crystalloidal  solutions.  A  similar  inter- 
pretation can  be  offered  of  the  local  concentration  which 
occurs  at  the  common  surface  of  adsorbing  solid  and 
solution. 

Noteworthy  in  this  connection  are  the  views  of 
Macallum,2  who  contends  that  surface  tension  is  a  prime 
factor  in  such  vital  phenomena  as  muscular  contraction, 
secretion  and  excretion,  and  cell  division,  and  traces 
differences  in  the  surface  tension  of  living  matter  by  a 
microchemical  study  of  the  distribution  of  inorganic  salts. 
Adsorption  of  Arsenious  Acid  by  Ferric  Hydroxide. 
— We  may  now  proceed  to  consider  cases  of  adsorption 
which  are  complicated  by  the  irreversibility  of  the  equili- 
brium or  the  intervention  of  chemical  affinity.  One 
interesting  case  where  chemical  affinity  may  be  a  factor, 
is  the  use  of  freshly  precipitated  ferric  hydroxide  as  an 
antidote  in  cases  of  arsenical  poisoning. 

The  power  of  ferric  hydroxide  to  remove  arsenious 
acid  from  its  solutions  has  generally  been  attributed 
to  the  formation  of  a  basic  ferric  arsenite,  but  Biltz 
has  found3  that  it  is  a  typical  case  of  adsorption. 

1  Proc.  Roy.  Soc.,  A,  1903,  72,  156. 

2  Brit.  Assoc.  Report,  1910,  740 ;  Proc.  Roy.  Soc.,  B,  1913,  86,  527. 

3  Ber.  deut.  chem.  Ges.t  1904,  37,  3138. 


ADSOEPTION  235 

When  the  hydroxide  is  shaken  with  a  solution  of 
arsenious  acid,  the  equilibrium  which  is  established  is 
reversible,  for  it  can  be  reached  from  both  sides. 
Experiments  in  which  a  definite  quantity  of  freshly 
precipitated  ferric  hydroxide  was  shaken  with  a  definite 
volume  of  solution  containing  different  amounts  of 
arsenious  acid  showed  that  if  x  is  the  equilibrium 
concentration  of  arsenious  acid  in  the  solution,  and  y 
the  corresponding  concentration  in  the  hydroxide,  then 

the    observations    are    in    harmony   with    the    formula 

i 
y  —  Kxl  .     That    is,   the   distribution    of   arsenious   acid 

between  water  and  precipitated  ferric  hydroxide  is 
essentially  the  same  as  the  distribution  of  acetic  acid 
between  water  and  carbon;  in  both  cases  the  removal 
of  the  dissolved  substance  from  the  solution  is  relatively 
complete  in  very  dilute  solution.  This  analogy  makes 
it  very  unlikely  that  the  removal  of  arsenious  acid 
from  solution  by  ferric  hydroxide  is  due  to  the  forma- 
tion of  a  compound,  and  the  fact  that  arsenious  acid 
in  aqueous  solution  has  a  normal  molecular  weight 
makes  it  impossible  to  regard  the  process  as  due  to 
the  formation  of  a  solid  solution.  Regarding  it,  on 
the  other  hand,  as  a  case  of  surface  condensation,  we 
can  understand  why  the  efficiency  of  ferric  hydroxide 
in  removing  arsenious  acid  from  solution  depends  on 
its  physical  condition. 

Adsorption  of  Dyes. — The  adsorbed  substances  so  far 
considered  have  been  crystalloids.  Many  of  the  most 
interesting  cases  of  adsorption,  however,  are  furnished 
by  organic  dyes,  some  of  which  in  aqueous  solution 
are  crystalloid  in  character,  while  others  are  colloidal. 
Walker  and  Appleyard1  were  able  to  show  that  when 
silk  is  dyed  with  picric  acid  a  real  equilibrium  is  attained 

1  Journ.  Chem.  Soc.,  1896,  69,  1334. 


236  PHYSICAL  CHEMISTRY 

which  is  independent  of  the  original  distribution ;  that 
is,  the  equilibrium  is  reversible.  They  showed  also 
that,  if  s  represents  the  equilibrium  concentration  of 
picric  acid  in  the  silk,  and  w  the  corresponding  con- 
centration in  the  water,  the  experimental  results  are 

satisfactorily  reproduced  by  the  formula  s  =  Kwpt  the 
usual  adsorption  formula. 

More  recently  it  lias  been  found  *  that  tho  same  general 
formula  represents  the  adsorption  of  crystal  violet  and 
patent  blue  by  carbon,  of  crystal  violet  and  patent 
blue  by  wool,  of  new  magenta  and  patent  blue  by 
silk,  and  of  crystal  violet  and  new  magenta  by  cotton. 
In  all  these  cases  the  adsorption  equilibrium  is  re- 
versible, and  it  is  remarkable  that  the  values  of  p 
(exclusive  of  the  cases  in  which  crystal  violet  was  used) 
all  Ho  between  4  and  7*7. 

So  far,  then,  as  these  experiments  go,  they  give  support 
to  the  view  that  the  process  of  dyeing  is  essentially  an 
adsorption  phenomenon,  not  depending  on  any  chemical 
affinity  between  the  dye  and  the  fibre,  or  consisting  in 
the  formation  of  a  solid  solution  in  the  fibre.  There  are, 
however,  a  number  of  observations  which  indicate  that 
other  factors  besides  adsorption  have  to  be  taken  into 
account  in  interpreting  the  relation  of  a  dye  to  the  fibre. 
The  very  fact  that  it  is  possible  to  get  a  fast  colour  in 
certain  cases  proves  that  the  equilibrium  between  dye 
and  fibre  is  not  always  reversible.  In  such  cases  one 
might  be  inclined  to  regard  the  process  as  a  chemical 
interaction  resulting  in  the  production  of  an  insoluble 
compound  of  the  nature  of  a  salt.  The  view  of  dyeing 
as  a  chemical  reaction  appears  to  be  supported  also  by 
the  observation  that  when  a  basic  colouring  matter  (that 
is,  an  organic  base  4-  an  inorganic  acid,  for  example, 

1  Frcundlich  and  Losev,  Zeit.  physikal^Vhem.,  1907,  59,  284. 


ADSORPTION  237 

magenta  or  crystal  violet)  is  employed  to  dye  wool, 
the  base  alone  is  taken  up  by  the  fibre,  while  the  acid 
is  left  in  the  solution.  In  spite  of  this,  the  colour  of 
the  dyed  fibre  is  that  of  the  salts  of  the  base.  All  this  is 
very  suggestive  of  chemical  action,  but  the  curious  thing 
is  that  a  similar  splitting  up  of  the  colouring  matter  into 
base  -f  acid  occurs  when  carbon  or  pure  cellulose  is  used 
in  place  of  wool.  In  these  cases  the  suggestion  of  salt- 
formation  cannot  be  accepted.  Altogether  the  problem  is 
a  very  complicated  one,  and  cannot  be  fully  discussed 
here.  It  appears  very  probable  that  the  splitting  up 
of  the  basic  dyes  which  has  just  been  mentioned  is  an 
electrical  phenomenon,  and  that  the  adsorption  pure  and 
simple  is  masked  to  some  extent.1  The  non-reversible 
character  of  the  equilibrium  between  dye  and  fibre  in 
some  cases  may  be  attributed  to  the  transformation  of  the 
free  base  deposited  on  the  fibre  into  a  tautomeric 
modification.2 

That  both  adsorption  and  chemical  action  may  be 
concerned  in  a  dyeing  process  is  shown  by  an  observa- 
tion recorded  by  Bayliss.3  If  well-washed  aluminium 
hydroxide  is  added  to  a  dilute  solution  of  the  blue  colloidal 
free  acid  derived  from  congo  red,  the  dye  is  taken  up 
by  the  suspended  hydroxide,  which  is  coloured  blue. 
If  this  blue  product  is  suspended  in  water  and 
warmed,  chemical  union  takes  place,  and  the  aluminium 
salt  of  congo  red  is  formed,  which  has  the  usual  red 
colour  of  the  salts. 

Attention  has  already  been  drawn  to  the  interesting 
fact  that  when  a  basic  colouring  matter  is  employed  to 
dye  wool  the  free  base  alone  is  taken  up  by  the  fibre, 

1  See  Michaelis  in  Koranyi  and  Richter's  Physikalitche  Cliemie  und 
Medizvn,,  vol.  ii.  p.  350. 
*  See  Freundlich  and  Losev,  loc.  cit.,  p.  301. 
8  Zeit.  Chem.  Ind.  KolL,  1908,  3,  224. 


238  PHYSICAL   CHEMISTRY 

while  the  acid  remains  in  solution.  The  fibre,  in  fact, 
decomposes  the  dye-salt  into  acid  and  base.  Other  cases 
where  colloids  have  this  effect  are  known.  In  the  fore- 
going chapter  it  was  pointed  out  that  when  a  colloidal 
solution  of  arsenious  sulphide  is  coagulated  by  the 
addition  of  barium  chloride  some  of  the  salt  is  decom- 
posed ;  the  coagulum  is  found  to  contain  barium,  while 
the  solution  contains  an  equivalent  quantity  of  hydro- 
chloric acid.  In  both  these  cases,  as  in  many  others,  the 
electrical  charge  on  the  solid  phase  is  the  main  factor 
in  determining  the  surface  equilibrium. 

Proteins  and  Adsorption. — The  previous  pages  will 
have  shown  how  very  common  is  the  phenomenon  of 
adsorption.  To  sum  up :  The  equilibrium  between  a 
solid  phase  and  a  solution  in  which  it  is  immersed  is 
frequently  characterised  by  a  local  concentration  of  the 
dissolved  substance  at  the  surface  of  the  solid  phase,  and 
in  the  majority  of  cases  it  is  impossible  to  interpret  this 
phenomenon  by  assuming  the  formation  of  a  solid  solution 
or  the  occurrence  of  a  chemical  reaction  between  solid 
and  dissolved  substance.  The  equilibrium  is  therefore 
described  as  an  adsorption  equilibrium,  and  one  of  its 
most  prominent  characteristics  is  the  fact  that  the 
amount  of  dissolved  substance  taken  up  by  the  solid 
increases  much  more  slowly  than  the  concentration  of  the 
solution ;  the  removal  of  the  dissolved  substance  is  there- 
fore relatively  most  complete  in  dilute  solution.  These 
facts  find  a  definite  expression  in  the  adsorption  formula : 

ct—p.  ctp  where  p  >  1. 

The  magnitude  of  the  adsorption  effect  will  of  course 
depend  on  the  surface  development  of  the  adsorbing  solid. 
Hence  it  is  that  carbon  in  the  form  of  charcoal  has  been 
so  largely  used  in  the  study  of  adsorption.  But  in  any 
case  where  the  surface  area  of  a  solid  is  relatively  great 


ADSORPTION  239 

for  its  volume,  the  conditions  are  favourable  for  the 
phenomenon  of  surface  condensation.  Whether  such  a 
solid  immersed  in  a  solution  will  exhibit  the  phenomenon 
will  naturally  depend  to  some  extent  on  the  nature  of  the 
dissolved  substance,  and  especially  on  its  electrical 
character.  Since  surface  development  is  a  preliminary 
condition  for  the  manifestation  of  adsorption,  and  since 
that  condition,  according  to  the  argument  at  the  be- 
ginning of  this  chapter,  is  satisfied  by  colloidally  dis- 
solved substances,  it  is  not  surprising  that  the  behaviour 
of  colloids  is  capable  in  many  cases  of  being  referred 
to  the  occurrence  of  adsorption  phenomena.  The  opinion 
has  rapidly  gained  ground  that  where  mixtures  of  colloids 
and  ions  are  involved,  as  in  the  living  cell,  the  equili- 
brium between  these  partakes  largely  of  the  nature  of 
an  adsorption  equilibrium.  In  such  a  complex  case 
it  is,  of  course,  impossible  to  say  exactly  what  part 
is  played  by  the  chemical  and  physical  factors  respec- 
tively, but  the  study  of  proteins  is  showing  that  these 
substances,  which  are  so  essentially  associated  with  the 
living  cell,  are  peculiarly  liable  to  exhibit  adsorption 
phenomena.  Not  only  are  proteins  readily  adsorbed 
by  charcoal,  mastic  suspension,  kaolin  suspension,  and 
freshly  precipitated  ferric  hydroxide,  but  they  themselves 
appear  to  adsorb  electrolytes  from  solution. 

There  are  many  grounds  for  the  conclusion  that  the 
experimental  behaviour  of  proteins  is  best  interpreted 
in  terms  of  adsorption.  One  of  the  lines  of  investigation 
which  lead  up  to  this  view  may  be  briefly  sketched  here. 
The  temperature  of  heat  coagulation  of  protein,  as 
recently  shown  by  Pauli,1  is  markedly  affected  by  traces 
of  salts.  The  protein  solution  used  by  this  investigator 
was  obtained  by  long-continued  dialysis  of  ox-blood 
serum,  and  exhibited  no  migration  in  an  electric  field; 
1  Zeit.  Chem.  Ind.  Koll.,  1908,  3,  2. 


240  PHYSICAL   CHEMISTRY 

the  protein  was  therefore  electrically  neutral.  When 
neutral  salts  of  the  alkali  or  alkaline  earth  metals  are 
added  in  very  small  quantity  to  such  a  protein  solution, 
so  that  the  concentration  of  the  salt  in  the  mixture  is 
not  above  0-05N,  the  temperature  of  heat  coagulation 
of  the  protein  is  raised  in  all  cases.  The  lower  the 
concentration  of  the  salt  solution,  the  greater  relatively 
is  the  extent  to  which  the  coagulation  is  inhibited.  If 
t0  is  the  temperature  of  heat  coagulation  for  the  protein 
solution  alone,  t  that  for  the  solution  of  protein  f  salt, 
and  c  is  the  concentration  of  the  added  salt,  then  it 
can  be  shown  that  the  experimental  data  are  in  harmony 
with  the  formula  t-t0  =  Kcm)  m<l,  which  is  obviously 
of  the  same  type  as  the  ordinary  adsorption  formula. 
Since  the  inhibiting  effect  is  not  produced  by  non- 
electrolytes,  and  since  the  effect  is  relatively  most 
marked  in  dilute  solution,  Pauli  concludes  that  there 
is  an  adsorption  equilibrium  between  the  protein  particles 
and  the  ions  of  the  salt,  and  that  the  change  thus 
brought  about  in  the  surface  of  the  protein  particles  is 
such  as  to  hinder  their  further  aggregation. 

Agglutination  as  an  Adsorption  Phenomenon. — One 

of  the  most  interesting  cases  in  which  the  adsorption 
formula  is  found  to  be  applicable  is  the  agglutination 
of  bacteria  by  immune  serum.  As  already  stated,  if 
the  serum  of  an  animal  which  has  previously  been  in- 
jected with  typhoid  bacteria  is  added  to  a  suspension 
of  these  bacteria,  the  latter  clump  together  and  settle 
to  the  bottom  of  the  containing  vessel.  On  examination 
the  bacteria  are  found  to  have  taken  up  a  certain  part 
of  the  agglutinin  contained  in  the  serum,  and  it  is  an 
interesting  question  what  is  the  relation  between-  the 
amount  of  agglutinin  taken  up  by  the  bacteria  and 
the  amount  which  remains  in  solution.  The  problem 


ADSOKPTION  241 

was  attacked  by  Eisenberg  and  Volk,1  who  added  a 
given  volume  of  agglutinin  solutions  of  different  con- 
centrations (obtained  by  diluting  the  serum  with  physio- 
logical salt  solution)  to  equal  quantities  of  suspensions 
of  typhoid  bacteria.  Equilibrium  is  reached  very  rapidly, 
and  the  distribution  of  the  agglutinin  is  ascertained  by 
centrifuging  and  then  examining  the  clear  liquid ;  a 
measure  of  the  agglutinin  left  in  this  clear  liquid  is 
obtained  by  finding  the  extent  to  which  it  must  be 
diluted  with  physiological  salt  solution  before  it  ceases 
to  produce  agglutination  under  given  conditions.  In 
this  way  a  uniform  measure  is  obtained  for  the  original 
agglutinin  solution  added  to  the  bacteria,  and  for  the  solu- 
tion which  has  come  into  equilibrium  with  the  bacteria. 

The  results  obtained  by  Eisenberg  and  Volk  for  the 
agglutination  of  typhoid  bacteria  by  agglutinin  are 
recorded  in  the  first  three  columns  of  the  following  table. 
The  figures  given  under  T  represent  the  quantities  of 
agglutinin  (in  arbitrary  units)  added  to  the  bacteria, 
while  those  under  S  (obs.)  represent  the  quantities  of 
agglutinin  left  in  the  solutions  after  the  agglutination  of 
the  bacteria.  B=T—  $  (obs.)  is  the  quantity  of  agglu- 
tinin taken  up  in  each  case  by  the  bacteria ;  the  figures 
under  S  (calc.)  are  obtained  in  a  manner  to  be  described 
presently. 

T.  B.  S(obs.).  S(calc.). 

220  0-02 

20  20  0  0-7 

40  40  0  2-1 

200  180  20  19'7 

400  340  60  52'9 

2,000  1,500  500  478 

10,000  6,500  3,500  3,890 

20,000  11,000  9,000  9,160 

These  figures  bring  out  a  feature  which  we  found  to 

i  Zeit.  Hygiene,  1902,  40,  155. 


242  PHYSICAL   CHEMISTRY 

be  characteristic  of  adsorption,  viz.  the  more  dilute 
the  solution,  the  more  completely  is  the  dissolved  sub- 
stance taken  up  by  the  solid  phase.  More  than  that, 
the  relation  betwen  B  and  S  is  satisfactorily  represented 
by  the  formula  B  =  KS$,  where  7T=24'7  for  the  whole 
series.  The  figures  given  in  the  last  column  of  the 
table  have  been  obtained  by  taking  the  numerical  value 
of  B  in  each  case,  and  calculating  S  by  means  of  the 
formula.  The  errors  of  observation  are  considerable,  and 
it  is  stated  that  it  is  impossible  to  determine  values  of 
S  below  1.  In  these  circumstances  the  agreement  be- 
tween the  observed  and  calculated  values  of  S  is  satis- 
factory, and  permits  the  conclusion  that  the  equilibrium 
between  bacteria  and  agglutinin  may  fairly  be  repre- 
sented by  a  formula  of  the  ordinary  adsorption  type.1 

The  applicability  of  the  foregoing  formula  to  the  dis- 
tribution of  agglutinin  between  typhoid  bacteria  and 
agglutinin  solution  was  first  demonstrated  by  Arrhenius, 
who  however  rejects  the  adsorption  theory,  and  main- 
tains that  the  agglutination  is  not  to  be  attributed  to 
a  special  surface  action.  He  believes  that  the  bacterial 
cell  contains  a  substance  which  is  a  good  solvent  for 
the  agglutinin,  and  draws  the  conclusion  that  the  mole- 
cular weight  of  the  agglutinin  in  this  solvent  is  two- 
thirds  of  the  molecular  weight  of  the  agglutinin  in  the 
surrounding  fluid.2 

It  is  doubtful  whether  it  is  permissible  to  regard  the 
applicability  of  the  empirical  adsorption  formula  as 
definitely  establishing  the  nature  of  the  equilibrium 
between  bacteria  and  agglutinin.  The  substances  in- 
volved are  complex,  and  there  are  one  or  two  facts 
which  suggest  eaution.  There  is,  firstly,  the  specificity 
of  the  agglutinins ;  that  is,  the  agglutinin  produced  by 

1  See  Craw,  Journ.  Hygiene,  1905,  5,  113. 

2  See  Immunochemistry,  p.  148. 


ADSORPTION  243 

injecting  an  animal  with  typhoid  bacteria  is  capable  of 
agglutinating  typhoid  bacteria  in  a  pre-eminent  degree. 
Such  a  fact  suggests  that  agglutination  may  be  something 
more  than  a  purely  physical  phenomenon.  Secondly, 
there  is  evidence  that  the  serum  of  an  animal  which 
has  been  inoculated  with  typhoid  bacteria  contains  not 
one,  but  several  agglutinins  of  different  degrees  of 
activity.  In  view  of  these  facts,  any  argument  as  to 
the  nature  of  agglutination  based  on  the  applicability  of 
the  adsorption  formula  appears  to  be  open  to  criticism. 


CHAPTER  XII 

CHEMICAL   EQUILIBRIUM    AND    THE    LAW 
OF   MASS    ACTION 

Reversible  Reactions. — The  chemical  reactions  employed 
for  the  purposes  of  analytical  chemistry  may  be  de- 
scribed as  '  complete '  reactions,  for  they  are  such  that 
they  proceed  until  one  or  other  of  the  reacting  com- 
pounds has  entirely  disappeared.  Suppose,  looking 
at  things  from  the  standpoint  of  the  analytical  chemist, 
we  take  the  change  on  which  the  ordinary  method  of 
detecting  and  estimating  silver  or  chloride  in  solution 
depends.  This  change  is  represented  by  the  equation 
AgN03-fNaCl  =  AgCl  +  NaN03,  and  it  is  well  known 
that  the  reaction  proceeds  until  either  the  silver  nitrate 
or  the  sodium  chloride  is  completely  removed;  short 
of  that  there  is  no  halt  in  the  reaction.  Similarly, 
the  reaction  between  hydrochloric  acid  and  sodium 
hydroxide  in  aqueous  solution  proceeds  until  either  one 
or  the  other  disappears;  they  cannot  exist  together  in 
the  same  solution.  It  is  noteworthy  that  such  complete 
reactions  are,  indeed  must  be,  non-reversible.  It  is 
impossible,  for  instance,  to  regenerate  silver  nitrate  and 
sodium  chloride  from  a  suspension  of  silver  chloride 
in  sodium  nitrate  solution,  certainly  not  to  an  extent 
which  can  be  detected  by  ordinary  analytical  methods. 

There  are,  however,  numerous  reactions  which  may 
be  described  as  '  incomplete ' :  they  do  not  proceed  until 
one  or  other  of  the  reacting  substances  has  completely 
disappeared.  The  reaction  stops  short  at  an  equilibrium 

244 


CHEMICAL  EQUILIBRIUM  245 

point  at  which  the  products  of  the  change,  and  the 
original  substances  as  well,  are  all  represented  in  the 
reaction  mixture.  Such  reactions,  too,  are  *  reversible  '  ; 
that  is,  the  substances  represented  on  the  right-hand 
side  of  the  equation  will,  if  brought  together,  react  to 
produce  the  substances  represented  on  the  left-hand 
side  of  the  equation;  further,  an  equilibrium  point  is 
reached  which,  provided  that  equivalent  quantities  of 
the  reagents  have  been  taken  in  both  cases,  is  the 
same  point  as  is  attained  by  starting  with  the  substances 
on  the  left  side  of  the  equation. 

An  illustration  of  such  reversibility  is  furnished  by 
the  reaction  between  hydrogen  and  iodine.  If  a  small 
quantity  of  iodine  is  introduced  into  a  glass  bulb,  and 
the  bulb  is  then  filled  with  hydrogen,  sealed  off  and 
expose*d  to  a  temperature  of,  say,  440°,  the  two  elements 
begin  to  combine.  After  an  hour  or  two,  however,  the 
reaction  stops,  and  if  the  bulb  is  cooled  and  opened, 
it  is  found  to  contain  hydrogen  iodide,  hydrogen,  and 
iodine.  If,  on  the  other  hand,  the  bulb  were  filled  with 
pure  hydrogen  iodide  and  kept  at  440°  until  no  further 
change  took  place,  it  would  be  found  that  the  bulb, 
when  cooled  and  opened,  contained  hydrogen  iodide, 
hydrogen,  and  iodine,  as  in  the  other  case.  The  reaction 
therefore  is  reversible,  and  this  fact  may  be  indicated  by 
substituting  oppositely  directed  arrows  for  the  usual  sign 
of  equality  in  the  equation  representing  the  change,  thus  : 


Another  standard  case  of  reversibility  is  the  reaction 
between  ethyl  alcohol  and  acetic  acid.  When  1  gram- 
mol.  of  ethyl  alcohol  is  mixed  with  1  gram-mol.  of 
acetic  acid,  a  reaction  takes  place  resulting  in  the 
formation  of  ethyl  acetate  and  water  ;  the  reaction, 
however,  is  incomplete,  and  stops  at  an  equilibrium 
point  at  which  the  reaction  mixture  contains  J  gram- 


246  PHYSICAL   CHEMISTRY 

mol.  alcohol,  J  gram-mol.  acid,  f  gram-mol.  ethyl 
acetate,  and  §  gram-mol.  water.  If,  on  the  other  hand, 
1  gram-mol.  of  ethyl  acetate  is  mixed  with  1  gram-mol. 
of  water,  a  reaction  sets  in  resulting  in  the  formation 
of  ethyl  alcohol  and  acetic  acid.  This  change  likewise 
stops  at  an  equilibrium  point  at  which  the  composition 
of  the  reaction  mixture  is  the  same  as  that  already 
stated.  Since  the  reaction  is  thus  reversible,  it  may  be 
written  C2H5OH+CH3.COOHJCH3.COOC2H5+H20. 

Law  of  Mass  Action  Applied  to  Reversible  Reac- 
tions.— The  law  of  mass  action  states  that  the  velocity 
of  a  chemical  reaction  is  proportional  to  the  molecular 
concentration  of  each  of  the  reacting  substances.  The 
line  of  proof  of  this  law  may  be  traced  by  considering 
a  reaction  which  takes  place  between  two  gases  A  and  B, 
and  by  looking  at  matters  from  the  molecular-kinetic 
standpoint.  In  such  a  case  the  reaction  can  take  place 
only  in  so  far  as  the  molecules  of  A  come  into  contact 
with  the  molecules  of  B.  The  velocity  of  the  reaction, 
therefore — that  is,  the  rate  at  which  A  and  B  disappear — 
will  be  proportional  to  the  frequency  of  the  collisions 
between  a  molecule  of  A  and  a  molecule  of  B,  even  al- 
though only  a  certain  proportion  of  the  collisions  is  fol- 
lowed by  chemical  interaction.  But,  on  kinetic  grounds, 
the  frequency  of  the  collisions  between  a  molecule  of  A 
and  a  molecule  of  B  is  proportional  to  the  product  of 
their  molecular  concentrations,  hence  it  follows  that  the 
velocity  of  reaction  between  A  and  B  is  proportional  to 
the  grodupjb  of  their  molecular  concentrations  (or  their 
'active  masses,'  as  it  is  sometimes  put).  A  similar  line 
of  argument  may  be  followed  in  the  case  where  A  and  B 
are  dissolved  substances. 

Suppose,  now,  that  we  are  dealing  with  a  reversible 
reaction,  represented  by  A-\-B  J  Ch-D,  and  suppose  that 
the  four  substances  are  mixed  together  so  that  in  the 


CHEMICAL   EQUILIBEIUM  247 

mixture  their  (molecular)  concentrations  are  a0,  &0,  CQ,  and 
d0  respectively.  If  these  are  not  the  proportions  corre- 
sponding to  the  equilibrium  point  a  reaction  will  take 
place,  from  left  to  right  or  vice  versd  according  to  the 
circumstances,  and  will  continue  until  equilibrium  is 
established.  The  velocity  of  the  reaction  may  obviously 
be  resolved  into  two  component  opposing  velocities,  firstly 
Vv  the  rate  at  which  A  and  B  are  reacting  to  form 
C  and  D,  and  secondly  F2,  the  rate  at  which  G  and  D 
are  reacting  to  form  A  and  B.  The  difference  between 
F]_  and  F2  is  the  observed  velocity  of  the  reaction.  Now, 
at  the  moment  of  mixing,  according  to  the  law  of  mass 
action,  F1  =  /:1a0&0  and  F2  =  £2e0d0,  where  7^  and  &2  are 
proportionality  factors,  so  that  the  observed  velocity 
immediately  after  mixing  is  Fx  —  F2  =  k^aJbQ  —  k2cQd0. 
After  the  reaction  has  proceeded  for  some  time,  and  has 
consequently  approached  the  equilibrium  position,  the 
values  of  the  concentrations  will  be  different,  say,  a,  b,  c, 
and  d.  The  velocity  of  the  reaction  will  therefore  now 
be  k^ab  —  k^cd.  If  the  reaction  has  proceeded  long  enough 
to  reach  the  equilibrium  point,  at  which  we  may  suppose 
the  concentrations  are  aei  le,  ce,  de,  then  the  velocity  of 
the  reaction  is  zero,  and  k1aebe  =  k$ede.  This  may  be  written 

j^  =  c-~  or  K—^-r,  where  K  is  a  constant  independent  of 
k2  aebe  afc 

the  concentrations  of  the  reacting  substances,  depending  < 
only  on  the  nature  of  the  reaction  and  the  temperature.  I 
./Tis  known  as  the  equilibrium  constant,  and  the  signifi-  j 
cance  of  the  equilibrium  formula  may  be  stated  in  the  | 
following  terms :   For  any  reversible  reaction  at  a  given 
temperature,  the  product  of  the  equilibrium  concentra- 
tions of  the  substances  on   the   right-hand  side  of  the 
equation  stands  in  a  constant  ratio  to  the  corresponding 
product  for  the  substances  on  the  left-hand  side. 

The    extent   to   which  this  application  of  the  law  of 


248  PHYSICAL   CHEMISTRY 

mass  action  to  reversible  reactions  is  verified  by  experi- 
ment is  best  appreciated  by  a  more  detailed  consideration 
of  the  reaction  between  ethyl  alcohol  and  acetic  acid : 
C2H6OH  +  CH3COOH  J  CH3.COOC2H5  +  H20.  It  has 
been  stated  already  that  the  equilibrium  system  reached 
after  mixing  1  gram-mol,  of  alcohol  and  1  gram-mol.  of 
acid  contains  J  gram-mol.  of  alcohol,  J  gram-mol.  of 
acid,  |  gram-mol.  of  ester,  and  f  gram-mol.  of  water.  If 
v  is  the  volume  of  the  system  at  the  point  of  equilibrium, 
then  the  molecular  concentrations  of  the  four  substances 

are  -,  *.  -,  and  *  respectively.     Hence  JT=  — *=]J— {  =  4. 
v1  v*  v  v  J  a,bt     l .  J 

/  V      V 

C  If,  now,  the  law  of  mass  action  is  strictly  applicable  to  this 
reversible  reaction,  then  we  ought  to  find  the  same  value  of 
K  even  when  the  initial  proportions  of  alcohol  and  acid 
are  quite  different.)  Suppose,  for  instance,  that  1  gram- 
molecule  of  acetic  acid  is  mixed  with  m  gram-molecules 
of  alcohol,  and  that  the  reaction  is  allowed  to  proceed 
to  "the  equilibrium  point.  If  x  is  the  fraction  of  a  gram- 
molecule  of  ester  which  is  present  in  the  equilibrium  mix- 
ture, then  the  corresponding  quantities  of  acid,  alcohol,  and 
water  are  1  -  x,  m  -  x,  and  x  respectively ;  further,  if  v  is 
the  volume  of  the  equilibrium  mixture,  the  concentrations 

of  acid,  alcohol,  ester,  and  water  are  -~-^,  ^^-,    —  and  - 

v  '      v        -v'          v 

respectively.     Applying  the  equilibrium  formula  we  ob- 

-•-  x2 

tain  K=^^  =  fr-^—y     The  value  of  x  is  ob- 

V  V 

tained  by  determining  the  amount  of  free  acetic  acid 
in  the  equilibrium  mixture ;  this  is  permissible,  since  the 
velocity  of  the  reaction  becomes  appreciable  only  at  high 
temperatures ;  at  the  ordinary  temperature  the  free  acid 
may  be  removed  by  neutralisation  without  the  back  re- 
action setting  in  to  any  appreciable  extent.  From  the 


CHEMICAL  EQUILIBRIUM  249 

known  values  of  m  and  x  it  is  then  possible  to  calculate 
K,  and  if  the  law  of  mass  action  is  valid,  the  value  so 
calculated  ought  to  be  the  same  as  that  obtained  with 
equivalent  quantities  of  the  reacting  substances.  There 
is,  however,  another  way  in  which  the  applicability  of 
the  law  may  be  tested,  namely,  by  taking  JT=4,  the 
figure  already  recorded,  and  calculating  for  each  value  of 
m  what  the  value  of  x  ought  to  be  on  the  basis  of  the 
equilibrium  formula.  The  comparison  of  the  values  of  x 
so  calculated  and  those  directly  observed  is  made  in  the 
following  table : — 

m.  a;  (found).  x(calc.). 

0-08  0-078  0-078 

0-28  0-226  0-232 

0-50  0-414  0-423 

0-07  0-519  0-528 

1-5  0-819  0-785 

2-24  0-876  0-864 

8-0  0-966  0-945 

The  excellent  agreement  of  the  figures  in  the  second 
and 'third  columns  demonstrates  the  applicability  of  the 
law  of  mass  action  to  the  reversible  reaction  between 
ethyl  alcohol  and  acetic  acid.  A  glance  at  the  table 
further  shows  that,  although  by  treating  acetic  acid  with 
the  equivalent  quantity  of  alcohol  it  is  possible  to  convert 
only  6 6 -6  per  cent,  of  the  acid  into  ester,  yet  by  using  a 
large  excess  of  alcohol  practically  the  whole  of  the  acid 
can  be  converted  into  ester.  Similarly,  the  first  line  of 
figures  in  the  table  shows  that  when  the  acid  is  in  large 
excess,  practically  the  whole  of  the  alcohol  is  converted 
into  ester. 

The  same  features  characterise  every  reversible  reaction. 
For  each  such  there  is  a  formula  with  a  characteristic 
constant  which  defines  the  relationship  between  the  re- 
acting substances  at  the  point  of  equilibrium. 


250  PHYSICAL  CHEMISTRY 

Application  of  the  Law  of  Mass  Action  to  Electro- 
lytes. Ostwald's  Dilution  Law.  —  On  the  ground  of 
evidence  submitted  in  earlier  chapters  the  view  has  been 
adopted  that  an  electrolyte  AS,  dissolved  in  water,  is 
to  a  greater  or  less  extent  dissociated  into  its  ions  A'  and 
B*,  and  that  the  degree  of  dissociation  increases  with 
dilution  of  the  solution.  The  equilibrium,  therefore, 
between  an  undissociated  electrolyte  and  its  ions  may 
be  shifted  in  one  direction  or  the  other  by  simply  diluting 
or  concentrating  the  solution.  The  process  of  dissociation 
is,  in  fact,  a  reversible  action,  and  may  be  represented  as 
AB^A'  -\-B\  As  Ostwald  pointed  out,  the  law  of  mass 
action  ought  to  be  applicable  in  such  a  case.  Suppose 
that  in  volume  V  of  the  solution  there  is  altogether  1 
gram-equivalent  of  electrolyte,  and  that  the  degree  of 
dissociation  is  a  ;  then  the  quantity  of  the  undissociaTed^ 
electrolyte^  stated  as  fraction  of  a  gram-  equivalent,  is 
1  -  a,  and  the  quantity  of  each  ion,  similarly  expressed, 

is   a;    the  concentrations   are  --   and   -     respectively. 


. 

The  equilibrium  formula  in  this  case  is  K—  ^f  =  (  ^ 

~V 

which  means  that,  according  to  the  law  of  mass  action, 
the  degree  of  dissociation  must  so  vary  with  the  dilution 

that  Q^gvp-  is  a  constant  for  the  particular  electrolyte 
chosen.     The  equation  K=  ,   ^^y  is  the  algebraic  ex- 

pression of  what  is  known  as  Ostwald's  Dilution  Law. 

As  an  example  of  a  case  where  the  validity  of 
Ostwald's  Dilution  Law  is  amply  verified,  we  may  take 
acetic  acid.  The  value  of  a,  which  is  required  for  the 
calculation  of  K,  is  most  easily  ascertained  by  deter- 
mining the  conductivity  as  described  in  Chapter  VII. 
The  values  of  a  so  deduced  for  s  number  of  acetic  acid 


CHEMICAL  EQUILIBRIUM  251 

solutions  containing  1  gram-equivalent  of  the  acid  in 
V  litres  are  recorded  in  the  following  table  ;  the  corre- 
sponding values  of  K  are  entered  in  the  last  column  :  — 


F.  a. 

0-994  0-004  1-62 

2-02  0-00614  1-88 

15-9  0-0166  1-76 

18-1  0-0178  1-78 

1500  0-147  1-69 

3010  0-205  1-76 

The  values  of  K  are  satisfactorily  constant,  for  it 
must  be  observed  that,  owing  to  the  very  character  of 
the  equilibrium  formula,  the  value  of  K  is  very  sensitive 
to  experimental  error.  Thus,  for  example,  if  a  for  the 
first  solution  had  been  found  to  be  0'0041  instead  of 
0-0040,  the  value  of  J5Txl05  would  have  been  1-70 
instead  of  1/62.  The  figure  usually  taken  as  the  value 
of  K  for  acetic  acid  —  the  '  dissociation  constant  '  —  is 
1-8  x  10~5  at  25°.  The  dissociation  constant  of  all  weak 
(that  is,  slightly  dissociated)  acids  and  weak  bases  may 
be  determined  in  a  similar  fashion,  but  it  is  remark- 
able that  for  strong  acids,  such  as  hydrochloric  acid, 
for  strong  bases,  such  as  sodium  hydroxide,  and  for 
neutral  salts,  such  as  potassium  nitrate,  the  value  of 

7z  -  r-fr  varies   resfularlv   with   dilution.     The   fact   that 

(l-a)K  * 

the  behaviour  of  strong  acids,  strong  bases,  and  neutral 
salts  is  not  in  harmony  with  Ostwald's  dilution  law 
has  not  yet  been  satisfactorily  explained,  and  indicates 
one  direction  in  which  the  electrolytic  dissociation  theory 
requires  to  be  supplemented. 

It  is  instructive  to  compare  the  values  of  K  obtained 
for  different  organic  acids.  A  few  typical  cases  are 
given  below.  It  is  noteworthy  how  the  introduction 
of  chlorine  into  the  acetic  acid  molecule  increases  the 


252  PHYSICAL   CHEMISTRY 

Acid.  K. 

Acetic 0-000018 

Monochloracetic .     .     .  0'00155 

Dichloracetic  ....  0-0514 

Formic 0-000214 

Benzoic 0-00006 

Salicylic 0-00102 

value  of  the  dissociation  constant;  the  much  greater 
value  of  K  for  salicylic  acid  as  compared  with  benzole 
acid  is  also  interesting. 

The  Strength  of  Acids. — The  occurrence  of  such 
notable  changes  in  the  value  of  K  from  one  acid  to 
another  raises  the  question  of  the  significance  of  the 

dissociation  constant.     As  already  stated.  K=  ,,^  .„,  so 

that  if  we  are  considering  two  acids  which  are  feebly 
dissociated,  for  which  therefore  1— a  is  practically  1, 
and  if  we  compare  the  two  acids  at  the  same  con- 

2  3 

centration,   we  have  K^  =  -L  and  K^  —  -^-.     From  this  it 

appears  that  the  value  of  K  for  an  acid  is  an  expres- 
sion of  its  inherent  ability  to  dissociate  into  its  ions. 
If,  now,  we  remember  that  all  acids  are  alike  in  splitting 
off  the  hydrogen  ion,  and  that  with  this  ion  are  associated 
all  those  properties  which  are  characteristic  of  acids  as 
a  class,  it  follows  that  the  dissociation  constant  of  an 
acid  is  a  measure  of  its  ability  to  exhibit  those  charac- 
teristic properties.  The  value  of  K,  in  other  words, 
is  a  measure  of  the  strength  of  the  acid.  If  this  is 
so,  then  the  order  of  the  acids  arranged  according  to 
their  values  of  K  ought  also  to  be  the  order  of  their 
strength  deduced  on  other  grounds.  This  turns  out  to 
be  the  case,  as  shown  by  the  investigations  of  Ostwald 
and  others.  The  strength  of  two  acids  may  be  compared 
by  allowing  them  to  compete  for-an  insufficient  quantity 
of  a  base,  and  then  to  determine,  from  the  volume 


CHEMICAL  EQUILIBRIUM  253 

changes  which  occur,  what  proportion  of  the  base  has 
been  appropriated  by  each  acid.  Or  the  effect  of  each 
acid  in  promoting  the  inversion  of  cane  sugar  may  be 
determined  (see  pp.  167,  277) ;  the  rate  of  this  change  is 
approximately  proportional  to  the  concentration  of  the 
hydrogen  ions  present,  and  may  be  employed  to  com- 
pare the  degrees  of  dissociation  of  two  acids  in  equi- 
valent concentration. 

That  a  base  is  shared  by  two  acids  in  proportions 
depending  on  their  relative  strength  is  an  important 
fact,  which  is  demonstrated  by  the  following  experi- 
ment. A  dilute  solution  of  the  sodium  salt  of  p-nitro- 
phenol  is  prepared,  and  equal  portions  of  the  solution 
are  put  in  three  test  glasses.  The  solution,  it  should 
be  noted,  has  an  intense  yellow  colour,  whereas  the 
p-nitrophenol  itself,  when  dissolved  in  distilled  water, 
gives  a  very  pale  yellow  solution.  Accordingly,  when 

standard   hydrochloric  acid,    say  -^,  is    gradually   added 

to  one  of  the  portions,  a  point  is  reached  at  which  the 
colour  is  almost  completely  discharged ;  this  is  the 
point  at  which  enough  hydrochloric  acid  (say  x  cub. 
cm.)  has  been  added  to  turn  out  practically  all  the 
p-nitrophenol  from  its  combination  with  the  soda ;  in 
competition  with  such  a  weak  acid  as  p-nitrophenol, 
hydrochloric  acid  is  able,  to  appropriate  practically  the 

whole    of    the    base.      If,    however,   x    cub.    cm.    of    — 

monochloracetic  acid  are  added  to  the  second  portion  of 
the  salt  solution,  the  colour  is  not  discharged ;  it  remains 
distinctly  yellow,  showing  that  in  competition  with 
monochloracetic  acid,  which  is  much  weaker  than  hydro- 
chloric acid,  p-nitrophenol  is  able  to  retain  some  of  the 
soda.  If  to  the  third  portion  of  the  sodium  salt  solution 

x   cub.   cm.     -   acetic  acid  are  added,  the  colour  of   the 


254  PHYSICAL   CHEMISTRY 

mixture  is  markedly  more  intense  than  in  the  second 
case,  for  now,  since  acetic  acid  is  comparatively  weak, 
the  p-nitrophenol  retains  an  appreciable  fraction  of  the 
available  soda. 

If  the  relative  strength  of  two  acids  has  been  deter- 
mined by  studying  their  influence  in  equivalent  con- 
centration on  the  rate  of  inversion  of  cane  sugar,  the 
figure  obtained  is  valid  only  for  the  concentration  in 
question.  That  this  must  be  so  is  evident  if  we  take 
the  particular  case  of  hydrochloric  and  acetic  acids. 
From  conductivity  data  it  follows  that  the  dissociation 
of  acetic  acid,  although  small,  increases  much  more 
rapidly  with  dilution  than  that  of  hydrochloric  acid, 
so  that  the  disparity  between  the  two  acids  in  regard 
to  their  content  of  hydrogen  ions  diminishes  with  in- 
creasing dilution.  Since  the  rate  of  inversion  of  cane 
sugar  is  approximately  proportional  to  the  concentration 
of  hydrogen  ions,  it  is  only  to  be  expected  that  the 

strength  of  ^  acetic  acid  (measured  in  terms  of  the 
effect  of  =-=  hydrochloric  acid  on  the  rate  of  sugar 
inversion)  is  greater  than  the  strength  of  —  acetic  acid 

(measured   in   terms   of   the   corresponding  effect   of  — 

hydrochloric  acid).  This  point  is  illustrated  by  the 
following  figures  for  the  relative  influence  of  hydro- 
chloric and  monochloracetic  acids  on  the  rate  of  inver- 
sion of  sucrose;  the  figure  for  hydrochloric  acid  is  in 
each  case  taken  as  100  : — 

5  Acid.  g  Acid. 

HC1  100  100 

CHoCl.COOH  5  14 

If  this  argument  is  followed  put,  it  is  obvious  that 
at  infinite  dilution  all  acids  would  be  equally  strong. 


CHEMICAL   EQUILIBRIUM  255 

Strength  of  an  Acid  as  Affected   by  its   Salts.— 

The  equilibrium  between  the  undissociated  molecule  of  a 
weak  acid  and  its  ions  is,  as  we  have  seen,  a  reversible 
one,  and  it  is  possible  therefore  to  shift  the  equilibrium 
in  either  direction  according  to  the  conditions.  The 
evidence  submitted  in  connection  with  the  reversible 
reaction  between  ethyl  alcohol  and  acetic  acid  showed 
that  the  greater  the  concentration  of  alcohol  in  the 
equilibrium  mixture  the  smaller  was  the  correspond- 
ing concentration  of  acetic  acid.  This  is  an  illustra- 
tion of  a  general  principle,  which,  if  applied  to  the 
equilibrium  between,  say,  acetic  acid  and  its  ions, 
CH3.COOHt;CH3.COO'  f  IT,  shows  that  by  increasing 
the  concentration  of  acetate  ions  the  concentration 
of  hydrogen  ions'  would  be  diminished.  It  is  easy  to 
increase  the  concentration  of  the  acetate  ions  by  add- 
ing sodium  acetate,  solutions  of  which  are  shown  by 
conductivity  data  to  be  highly  dissociated.  We  should 
therefore  expect  that  an  acetic  acid  solution  to  which 
sodium  acetate  has  been  added  would  contain  fewer, 
hydrogen  ions  than  an  equally  concentrated  solution 
of  acetic  acid  to  which  no  sodium  acetate  has  been 
added ;  the  acid  effect  would  be  weakened  by  the  pre- 
sence of  a  neutral  salt  of  the  acid.  This  conclusion 
is  strikingly  verified  by  the  figures  given*  in  the  follow- 
ing table.1  F  represents  the  rate  of  inversion  of  sucrose 

•vr 

under   the    influence    of    —  CH3COOH   in    presence    of 

gradually  increasing  quantities  of  sodium  acetate :  the 
actual  method  by  which  Fis  determined  will  be  described 
later,  and  for  the  present  it  may  simply  be  taken  as  a 
measure  of  the  concentration  of  hydrogen  ions  in  the 
acetic  acid  solution.  The  numbers  in  the  column 

1  Arrhenius,  Zeit.  physical.  Chem.,  1890,  5,  1. 

R 


256  PHYSICAL  CHEMISTRY 

headed  V  obs.  show  that,  in  accordance  with  the  argu- 
ment outlined  above,  the  concentration  of  hydrogen 

ions  in  —  CH3COOH  diminishes  steadily  as  the  con- 
centration of  sodium  acetate  in  the  same  acetic  acid 
solution  is  increased.  More  than  that,  it  is  possible, 
on  the  basis  of  the  equilibrium  formula,  to  calculate 
the  concentration  of  hydrogen  ions  in  each  solution,  and 
therefrom  to  calculate  the  velocity  of  inversion  under 
the  influence  of  that  solution;  the  values  so  obtained 
are  tabulated  under  V  calc. 

Inverting  Solution.  Fobs.  V  calc. 

^CH3OOOH  0-75 

„  +  |>CH3COONa  0-122  0-129 

+  40          „  0-070  0-070 

„  +2Q          „  0-040  0-038 

„  +^          „  0-019  0*017 

„  +^          „  0-0105  0-0100 

The  agreement  between  the  observed  and  calculated 
values  is  striking  evidence  in  favour  of  the  electrolytic 
dissociation  theory,  which  is  involved  in  the  calculation. 

It  must,  however,  be  pointed  out  that  such  a  calculation 
cannot  be  successfully  made  for  the  influence  of  neutral 
salts  on  the  inverting  efficiency  of  strong  acids.  In 
one  sense  this  is  not  strange,  since,  as  already  indicated, 
Ostwald's  dilution  law  is  not  valid  for  these.  But  the 
influence  of,  say,  sodium  chloride  on  the  activity  of 
hydrochloric  acid  is  not  even  qualitatively  in  agreement 
with  what  we  should  expect  on  the  basis  of  the  electro- 
lytic dissociation  equilibrium.  The  rate  at  which  sucrose 
is  inverted  by  hydrochloric  acid  is  increased  by  the  addition 


CHEMICAL   EQUILIBKIUM  257 

of  a  neutral  chloride,  an  effect  that  is  generally  referred 
to  as  '  neutral  salt  action.'  The  magnitude  of  the  effect 
is  considerable,  for  Arrhenius  has  shown  that  the  rate 
of  inversion  of  a  10  per  cent,  sucrose  solution  by 
0-05NHC1  is  increased  by  about  25  per  cent,  when  the 
solution  is  also  O4N  in  relation  to  sodium  chloride. 
Other  neutral  chlorides  exert  a  like  accelerating  influence. 
Neutral  salt  action  has  not  yet  been  satisfactorily  ex- 
plained, although  numerous  attempts  have  been  made ; l 
Arrhenius,  for  instance;  suggests  that  neutral  salts 
increase  the  osmotic  pressure  of  the  sucrose,  while 
Caldwell 2  regards  neutral  salt  action  as  a  concentrat- 
ing effect  brought  about  by  the  hydration  of  the  salt. 
In  any  case,  some  factor  is  involved  in  neutral  salt 
action  of  which  the  electrolytic  dissociation  theory,  in 
its  original  form  at  least,  takes  no  cognisance. 

Reactions  between  Ions. — The  influence  of  sodium 
acetate  or  any  other  neutral  acetate  in  repressing  the 
dissociation  of  acetic  acid  is  one  example  of  the  ionic 
reactions  which  occur  when  solutions  of  electrolytes  are 
mixed,  and  of  which  only  indirect  evidence  can  be  ob- 
tained. If  a  little  concentrated  sodium  acetate  solution 
is  added  to  a  solution  of  hydrochloric  acid  nothing  obvious 
happens,  but  indirect  evidence  can  be  obtained  showing 
that  a  reaction  does  indeed  take  place,  which  results  in 
the  almost  complete  removal  of  the  hydrogen  ions  from 
the  solution.  If,  for  instance,  sulphuretted  hydrogen 
water  is  added  to  a  solution  of  ferrous  sulphate  which 
has  been  acidified  with  hydrochloric  acid,  no  precipitate 
is  produced ;  on  the  further  addition,  however,  of  a  little 
concentrated  sodium  acetate  solution,  a  black  precipitate 
of  ferrous  sulphide. is  thrown  down  immediately.  The 

1  See  Senter,  Journ.  Chem.  Soc.,  1907,  91,  462. 

2  Proc.  Roy.  Soc,,  A,  1906,  78,  272. 


258  PHYSICAL   CHEMISTRY 

sodium  acetate  impairs  the  acid  effect  of  the  hydrochloric 
acid,  and  a.  consideration  of  the  phenomenon  from  the 
point  of  view  of  electrolytic  dissociation  leads  to  an 
intelligible  explanation.  When  hydrochloric  acid  and 
sodium  acetate,  both  highly  dissociated  electrolytes,  are 
mixed  in  aqueous  solution,  opportunity  is  given  for  the 
formation  of  two  other  electrolytes,  namely,  sodium 
chloride  and  acetic  acid,  the  first  of  which  is  highly, 
the  second  feebly,  dissociated.  As  we  have  seen  already, 
the  dissociation  constant  of  acetic  acid  is  low,  which 
means  that  acetate  ions  and  hydrogen  ions  can  exist 
alongside  each  other  only  to  a  certain  small  extent,  de- 
fined by  the  said  dissociation  constant.  Hence  when 
hydrochloric  acid  and  sodium  acetate  are  mixed,  the 
acetate  ions  and  hydrogen  ions  unite  almost  completely 
to  form  undissociated  acetic  acid,  and  the  concentration 
of  free  hydrogen  ions  is  still  further  diminished  if  excess 
of  sodium  acetate  is  added  to  the  hydrochloric  acid.  If 
we  make  the  assumption,  which  is  not  very  far  from 
the  truth,  that  hydrochloric  acid,  sodium  acetate,  and 
sodium  chloride  are  almost  completely  dissociated,  while 
acetic  acid  is  dissociated  to  a  negligible  extent,  the 
main  course  of  the  ionic  reaction  in  question  is  expressed 
by  the  equation 


The  addition  of  sodium  acetate  to  hydrochloric  acid  thus 
effects  a  removal  of  the  hydrogen  ions,  and  so  amounts 
practically  to  a  neutralisation  of  the  great  bulk  of  the 
hydrochloric  acid.  The  sodium  salt  of  any  weak  acid 
would  do  quite  as  well  as  sodium  acetate  ;  if,  for  instance, 
a  strong  solution  of  borax  is  added  to  a  solution  con- 
taining ferrous  sulphate,  sulphuretted  hydrogen  water, 
and  a  little  free  hydrochloric  acid,  a  black  precipitate 


CHEMICAL   EQUILIBRIUM  259 

is  produced  immediately.  The  explanation  of  this 
effect  is  the  same  as  that  given  in  the  case  of  sodium 
acetate. 

Another  ionic  reaction  which  occurs  on  mixing  two 
electrolytes  which  have  no  common  ion  is  the  union 
of  the  hydrogen  and  hydroxyl  ions.  These  ions  cannot 
exist  alongside  each  other  except  in  the  minutest  quan- 
tities (see  p.  170),  so  that  the  process  of  neutralisation 
of  hydrochloric  acid  (or  any  other  strong  acid)  by  sodium 
hydroxide  (or  any  other  strong  base)  may  be  represented 
by  the  equation:  H'  +  Cl'+Na'+OH^HgO+Cl'+Na". 
The  similarity  between  this  neutralisation  and  the 
result  of  adding  sodium  acetate  to  hydrochloric  acid  is 
apparent.  tWi 

Just  as  the  equilibrium  between  acetate  ions,  hydrogen 
ions,  and  undissociated  acetic  acid  is  defined  by  the 
dissociation  constant  for  acetic  acid,  so  the  extent  to 
which  hydrogen  and  hydroxyl  ions  can  exist  alongside 
each  other  in  water  is  similarly  fixed.  If  we  apply  the  law 

of  mass  action  to  the  equilibrium  HgO^H*  +OH' we  obtain 

o  o 

j£__    H.  oii^  wjiere  QHj  QQH)  an(^  QH90  are  tjie  concentra- 

H2° 

tions  of  the  hydrogen  ion,  the  hydroxyl  ion,  and  water 
respectively.  Since  the  concentrations  of  the  ions  are 
extremely  small,  that  of  the  water  may  be  taken  as  in- 
dependent of  their  variations,  so  that  CH.C0H  =  ^j  another 
constant.  This  means  that  the  product  of  the  concen- 
trations of  the  hydrogen  and  hydroxyl  ions  in  any  aqueous 
solution  must  be  a  constant.  Several  lines  of  evidence  lead 
to  the  figure  l'2xlO~14  being  taken  as  the  value  of  k 
at  25°  (compare  pp.  172  and  317). 

If  water  contains  both  hydrogen  and  hydroxyl  ions 
in  equivalent  quantities,  it  may  be  regarded  as  a  very 
weak  acid  or  as  a  very  weak  base,  so  that  when  a 
neutral  salt  AB  is  dissolved  in  the  water — a  salt  which 


260  PHYSICAL   CHEMISTRY 

is  largely  dissociated  into  its  ions  A'  and  B*  — there  is 
the  possibility  of  ionic  reactions  taking  place  which 
result  in  the  formation  of  two  new  undissociated  com- 
pounds, HA  and  BOH.  The  extent  to  which  this  takes 
place  will  depend  on  the  strengths  of  the  acid  and  the 
base.  If  they  are  both  very  strong,  as  would  be  the 
case  if  AB  stood  for  NaCl,  the  quantities  of  HA  and 
BOH  formed  will  be  very  small,  and  approximately 
equal  quantities  of  hydrogen  and  hydroxyl  ions  will  be 
removed  for  the  purpose.  This  removal  of  hydrogen 
and  hydroxyl  ions  is  made  good  by  the  dissociation  of 
a  small  quantity  of  water,  in  order  to  maintain  the 
condition  Cn.CoH  =  l'2  X  10  "u.  Suppose,  however,  that 
HA  is  a  weak  acid,  while  BOH  is  a  strong  base — as 
would  be  the  case  if  AB  stood  for  borax — then  from  the 
ions  A7,  B',  H',  and  OH'  more  undissociated  HA  will  be 
formed  than  undissociated  BOH,  and  there  will  no  longer 
be  equivalent  quantities  of  hydrogen  and  hydroxyl  ions. 
Although  to  maintain  the  condition  Cn.C0H  =  1*2  X  10  ~14 
a  little  water  will  dissociate,  this  cannot  get  rid  of 
the  excess  of  hydroxyl  ions;  the  solution  will  therefore 
have  an  alkaline  reaction.  In  harmony  with  this  it  is 
found  that  borax,  however  carefully  it  is  purified, 
always  gives  an  alkaline  reaction  when  dissolved  in 
water.  Other  salts  which  behave  in  a  similar  way,  since 
they  are  derived  from  a  strong  base  and  a  weak  acid, 
are  potassium  cyanide  and  sodium  carbonate. 

If  the  salt  AB,  on  the  other  hand,  is  such  that  HA 
is  a  strong  acid,  while  BOH  is  a  weak  base,  the  solution 
of  the  salt  must  have  an  acid  reaction.  The  argument 
which  leads  to  this  conclusion  is  parallel  to  that  already 
given.  The  case  where  a  salt,  however  carefully  purified, 
gives  an  acid  reaction  when  dissolved  in  water  is  illustrated 
by  aniline  hydrochloride. 

The    phenomenon    of    a    neutral    salt    reacting    with 


CHEMICAL  EQUILIBRIUM  261 

water  so  as  to  give  either  an  acid  or  an  alkaline 
reaction  is  known  as  '  hydrolytic  dissociation.'  If  we 
wish  to  determine  the  extent  of  hydrolytic  dissocia- 
tion in  any  given  case,  we  observe  the  influence  of 
the  salt  on  the  rate  of  inversion  of  sucrose  or  on  the 
rate  of  saponification  of  ethyl  acetate  (see  p.  283).  The 
first  of  these  methods  is  employed  when  the  salt  in 
question  is  derived  from  a  strong  acid  and  a  weak  base, 
the  second  when  it  is  derived  from  a  strong  base  and 

a  weak  acid.     In  this  way  it  has  been  found  that  in  =^ 

solution  at  25°  sodium  carbonate  is  hydrolytically  dis- 
sociated to  the  extent  of  3-17  per  cent.,  potassium 
cyanide  1-12  per  cent.,  borax  0'05  per  cent.,  aniline 
hydrochloride  1*5  per  cent. 

Amphoteric  Electrolytes. — Water  has  been  described 
above  as  an  electrolyte  which  yields  at  the  same  time 
hydrogen  and  hydroxyl  ions.  There  is  an  interesting 
class  of  substances  which  in  this  respect  resemble  water, 
and  are,  further,  of  considerable  importance  in  connection 
with  the  behaviour  of  proteins.  The  class  referred  to 
is  that  of  the  amino-carboxylic  acids,  substances  which 
contain  at  least  one  NH2-group  and  one  COOH-group, 
and  are  therefore  capable  of  acting  as  bases  or  as  acids 
according  to  circumstances ;  in  view  of  this  double 
character  they  are  termed  '  amphoteric '  electrolytes. 
Such  an  electrolyte  will  have  two  dissociation  constants, 
one  corresponding  to  its  acid  function,  the  other  to  its 
basic  function.  It  is  further  capable  of  forming  two 
series  of  salts,  one  series  by  combining  with  acids,  the 
other  series  by  combining  with  bases. 

Just  as  ammonia,  when  dissolved  in  water,  exists, 
to  some  extent  at  least,  in  the  form  of  the  compound 
NH4OH,  so  it  is  supposed  that  glycine,  which  may  be 
taken  as  an  example  of  an  ammo-acid,  forms  in  water 


262  PHYSICAL   CHEMISTRY 

CH2.NH  .OH 

the  compound    |  .    The   ions   produced   by   the 

COOH 
dissociation  of  this  compound  are 

CH2.NH3',     CH2.NH3.OH,  CH2.NH3* 

OH',H',     |  ,      |  and   |  ; 

COOH  COO'  COO' 

the  last  mentioned  results  from  the  simultaneous  splitting 
off  of  hydrogen  and  hydroxyl  ions,  and  corresponds  really 
to  an  intramolecular  salt.  The  concentrations  of  all 
these  ions  are  exceedingly  small  in  an  ordinary  aqueous 
solution  of  glycine ;  the  acid  and  basic  groups  present  in 
the  molecule  are  antagonistic,  and  the  result  is  that 
glycine,  whether  regarded  as  acid  or  base,  is  very  weak. 
A  similar  statement  applies  to  all  amino-carboxylic  acids. 
This  being  so,  it  is  clear  that  the  salts  of  such  an 
amphoteric  electrolyte,  both  with  a  strong  acid  and 
a  strong  base,  will  be  liable  to  hydrolytic  dissociation. 
Suppose  that  HROH  represents  the  formula  of  an 
amino-carboxylic  acid,  and  that  the  sodium  salt  NallOH 
and  the  chloride  HRC1  have  been  prepared ;  this  is 
possible,  since  the  amino-carboxylic  acid  acts  as  an  acid 
towards  sodium  hydroxide  and  as  a  base  towards  hydro- 
chloric acid.  The  salt  NaROH,  being  derived*  from 
a  strong  base  and  a  weak  acid,  will  be  hydrolytically 
dissociated  in  aqueous  solution,  an  effect  which  may  be 
regarded  as  brought  about  by  an  interaction  between 
water  and  the  negative  ion  of  the  salt,  thus : 

ROH'+H20;±HROH  +  OH'. 

The  hydrolytic  dissociation  results,  therefore,  in  the 
negative  ion  ROH'  being  replaced  to  some  exter\t  by  the 
OH'  ion.  The  ionic  conductivity  of  the  hydroxyl  ion 
is  much  greater  than  that  of  any  other  anion,  hence  one 
result  of  the  hydrolytic  dissociation  of  NaROH  is  that 
the  conductivity  of  the  solution^  is  exceptionally  high. 
A  determination  of  the  conductivity^niay  in  fact  be  used 


CHEMICAL  EQUILIBRIUM  263 

to  calculate  the  extent  of  the  hydrolytic  dissociation. 
This  may  be  ascertained  also  by  studying  the  influence 
of  the  salt  NaROH  on  the  rate  of  saponification  of 
ethyl  acetate,  which,  as  already  stated,  is  a  measure  of  the 
hydroxyl  ion  concentration.  The  extent  of  hydrolysis 
of  the  salt  NaROH  having  been  ascertained  by  one 
or  other  of  these  methods,  it  is  possible  to  calculate  the 
acidic  dissociation  constant  ka  of  HROH ;  the  way  in 
which  this  is  done  cannot  be  discussed  here. 

Similarly,  by  determining  the  conductivity  of  the 
salt  HRC1,  or  by  studying  its  influence  on  the  rate  of 
inversion  of  sucrose,  the  extent  of  hydrolytic  dissociation 
in  this  case  can  be  ascertained,  and  the  basic  dissociation 
constant  kb  deduced  therefrom.  For  amino-carboxylic 
acids  it  is  found  generally  that  ka  is  greater  than  kb ; 
that  is,  the  acidic  character  of  these  compounds  is  more 
strongly  developed  than  their  basic  character.  The 
following  figures  may  be  quoted  in  support  of  this 
statement : l — 

*a(25°)  kb  (25°). 

Glycine 1-8   x  10-™  27    x  10~12 

Sarcosine 1'2   x  10'10  17   x  1Q-12 

Alanine 1-9   x  10"10  5'1    x  10~12 

Leucine 1-8    x  1Q-10  2-3   xlO'12 

/3-Asparagine     .     .     .  1-35  x  lO'9  1 -53x10-" 

The  values  for  ka  recorded  in  the  table  are  about  the 
same  as  Jca  for  phenol,  so  that  the  acidic  character  of 
all  these  amino-carboxylic  compounds  is  exceedingly 
feeble.  Their  basic  character  is  still  less  marked  ;  the 
values  of  kb  in  the  table  are  roughly  about  one-hundredth 
of  the  corresponding  figure  for  aniline. 

In  the  case  of  a  sparingly  soluble  amphoteric  electro- 
lyte, its  peculiar  character  is  clearly  indicated  by  the 
influence  of  acids  and  alkalis  on  its  solubility.  A  spar- 
ingly soluble  base,  ^aniline  for  instance,  is  more  soluble 

1  See  Lunden,  Zeit.  physikal.  Chcm.,  1906,  54,  561. 


264  PHYSICAL   CHEMISTRY 

in  dilute  hydrochloric  acid,  but  not  more  soluble  in 
dilute  sodium  hydroxide,  than  it  is  in  water.  A  spar- 
ingly soluble  acid,  salicylic  acid  for  instance,  is  con- 
versely more  soluble  in  dilute  sodium  hydroxide,  but 
not  more  soluble  in  dilute  hydrochloric  acid,  than  it  is 
in  water.  We  should  expect  therefore  that  the  solu- 
bility of  a  sparingly  soluble  amphoteric  electrolyte, 
which  functions  both  as  acid  and  as  base,  would  be 
increased  by  adding  either  acid  or  alkali.  This  turns 
out  to  be  the  case,  as  has  been  shown,  for  instance, 
in  the  case  of  theobromine.  Paul  found 1  that  one  part 
of  theobromine  required  for  its  solution  3282  parts  of 

water  at  18°,  2125  parts  of  ^HCl,   or   22-93   parts   of 

— NaOH.      The    solubility   of    theobromine    in    acid    is 

little  greater  than  its  solubility  in  water,  which  means 
that  the  hydrochloride  is  hydrolytically  dissociated  to  a 
very  large  extent,  and  that  the  basic  character  of 
theobromine  is  therefore  feebly  developed.  As  is 
evident  from  the  comparative  solubility  in  sodium 
hydroxide,  the  acidic  character  of  theobromine  is  well 
marked ;  ka  in  this  case  is  If33xl0~8. 

There  is  every  reason  to  believe  that  the  polypeptide 
group  forms  an  essential  part  of  the  protein  molecule,2 
and  as  polypeptides  are  built  up  by  the  condensation  of 
amino-carboxylic  acids,  there  is  good  ground  for  regard- 
ing the  proteins  as  amphoteric  electrolytes.  In  many 
respects  their  behaviour  is  in  harmony  with  this  con- 
ception of  their  character.  There  is,  for  instance,  the 
observation,  due  originally  to  Hardy  and  confirmed  by 
Pauli,3  that  neutral  protein  acquires  electro-positive  char- 
acteristics on  the  addition  of  acids,  as  shown  by  its 

1  Arch.  Pharm.,  1901,  239,  48. 

2  See  Schryver,  The  General  Characters  of  the  Proteins. 

3  Hofmeister's  Beitr.,  1906,  7,  531. 


CHEMICAL  EQUILIBRIUM  265 

migration  towards  the  cathode  in  an  electric  field, 
while  it  acquires  electro-negative  characteristics  on  the 
addition  of  alkali. 

Further  support  for  the  view  that  protein  is  an  am- 
photeric  substance  is  furnished  by  the  work  of  Bugarszky 
and  Liebermann,1  who  studied  the  effect  of  adding  egg 
albumin  to  0'05N  solutions  of  hydrochloric  acid,  sodium 
hydroxide,  and  sodium  chloride.  The  effect  was  measured 
by  determining  the  freezing  points  of  the  electrolyte 
solutions  (1)  without  any  albumin,  (2)  after  the  addition 
of  various  quantities  of  albumin.  Some  of  the  results 
obtained  are  incorporated  in  the  following  table,  the  first 
column  giving  the  weight  (g)  of  albumin  added  to 
100  cub.  cm.  of  the  electrolyte  solution,  while  the 
three  succeeding  columns  give  the  observed  depressions 
(A)  of  the  freezing  point : — 

g.  A  for  0-05N  HC1.  A  for  0'05N  NaOH.  A  for  0'05NNaCl. 

0  0-186°  0-181°  0-183° 

0-8  0-172°  0-162°  0-191° 

1-6  0-146°  0-151°  0-194° 

3-2  0-107°  0-116°  0-199° 

6-4  0-087°  0-097°  0-203° 

The  depression  of  the  freezing  point  in  the  case  of 
sodium  chloride  is  increased  by  the  addition  of  albumin, 
and  the  amount  of  the  increase  is  practically  equal  to 
the  depression  which  the  albumin  produces  by  itself; 
thus  a  solution  containing  6 -4  grams  of  egg  albumin 
in  100  grams  of  water  had  a  freezing  point  0'022°  below 
that  of  water.  The  effect  of  egg  albumin  011  the  freezing 
points  of  O'OoN  hydrochloric  acid  and  sodium  hydroxide 
is  obviously  quite  a  different  phenomenon.  The  de- 
pression of  the  freezing  point  produced  by  the  given 
quantity  of  acid  or  alkali  diminishes  markedly  as  the 
quantity  of  added  albumin  increases.  This  shows  clearly 

1  Pfliiger'a  Arch.,  1898,  72,  51. 


266  PHYSICAL   CHEMISTEY 

that  the  number  of  molecules  originally  present  in  the 
acid  or  alkali  solution  has  decreased,  and  this  must 
be  due  to  the  ability  of  both  acid  and  alkali  to  form 
complex  molecules  with  the  albumin. 

Dissociation  Equilibrium  in  a  Saturated  Solution 
of  an  Electrolyte. — The  systems  to  which  we  have 
hitherto  applied  the  law  of  mass  action  have  been 
homogeneous — mainly  solutions  of  electrolytes.  It  will 
be  interesting  now  to  see  in  what  way  the  law  works 
out  when  applied  to  a  non-homogeneous  system,  con- 
sisting, say,  of  a  saturated  solution  of  an  electrolyte  in 
contact  with  excess  of  the  solid  substance.  Suppose 
we  take  the  case  of  benzoic  acid,  an  electrolyte  to 
which  Ostwald's  dilution  law  is  applicable.  In  a 
saturated  solution  of  this  acid  we  have  equilibrium 
between  the  undissociated  molecules  and  the  ions,  as 
represented  by  the  following : 

C6H5.COOH  ^  C6H6.COO'+IT. 

There  is  however  this  peculiarity,  that  we  cannot  alter 
the  concentration  of  the  undissociated  molecules  so 
long  as  the  temperature  remains  constant,  for  by  sup- 
position the  solution  is  saturated  with  benzoic  acid, 
and  is  in  contact  with  solid  benzoic  acid.  Thus  if  any- 
thing happened  to  increase  the  concentration  of  the 
undissociated  molecules,  this  would  simply  lead  to  an 
equivalent  removal  of  acid  from  solution.  If  anything 
happened  to  diminish  the  concentration  of  the  undis- 
sociated molecules,  fresh  acid  would  dissolve  until  the 
said  concentration  was  brought  up  to  its  saturation 
value.  That  is  to  say,  the  concentration  or  active 
mass  of  the  undissociated  benzoic  acid  molecules  in  the 
above  dissociation  equilibrium  is  constant,  so  long  as 
there  is  excess  of  benzoic  acid  present  and  the  tempera- 
ture remains  constant.  The  application  of  the  law  of 


CHEMICAL  EQUILIBRIUM  267 

mass  action  to  the  equilibrium  between  benzoic  acid 
and  its  ions  leads  to  K=c-^2,  where  cx  and  c2  are  the 

concentrations  of  the  ions,  and  c  is  that  of  the  un- 
dissociated  molecules.  As  has  just  been  explained. 
c  is  constant  under  the  specified  conditions,  so  that 
0^2  =  const.  Naturally,  so  long  as  the  solution  contains 
nothing  but  benzoic  acid,  ^  =  0%,  but  if  the  equilibrium 
between  benzoic  acid  and  its  ions  is  displaced  by  the 
introduction  of  other  electrolytes,  c^  will  be  different 
from  c2;  even  then,  however,  the  law  of  mass  action 
requires  the  condition  CjC2  =  const,  to  be  fulfilled.  This 
means  that  for  any  solution  which  is  kept  saturated 
with  benzoic  acid  at  a  given  temperature  the  product 
of  the  concentrations  of  the  ions  remains  constant,  how- 
ever their  individual  values  may  vary.  This  product 
of  the  ionic  concentrations  in  a  saturated  solution  is 
generally  known  as  the  *  solubility  product.' 

In  considering  the  conditions  which  define  the  equi- 
librium in  a  saturated  solution  of  a  sparingly  soluble 
electrolyte  we  have  taken  a  special  case.  This  case, 
however,  serves  to  bring  out  two  general  principles 
involved  in  a  non-homogeneous  equilibrium ;  these  may 
be  stated  as  follows:  (1)  The  active  mass  or  concen- 
tration of  any  solid  concerned  in  a  non-homogeneous 
equilibrium  is  constant  for  a  given  temperature;  (2)  for 
any  dissociation  equilibrium  in  a  saturated  solution 
the  product  of  the  concentrations  of  the  dissociated 
parts  is  a  constant  for  a  given  temperature.1 

One  or  two  consequences  of  the  application  of  these 
principles  to  saturated  solutions  of  electrolytes  are  worth 
noting.  If  the  product  of  the  ionic  concentrations 
CjCg  is  to  remain  constant,  anything  which  leads  to  an 
increase  of  c2  must  mean  a  diminution  of  cr  Now, 
as  pointed  out  in  the  previous  part  of  this  chapter, 
1  See,  however,  Kendall,  Proc.  Roy.  Soc.,  A,  1911,  85,  200. 


268  PHYSICAL  CHEMISTRY 

it  is  possible  to  increase  the  concentration  of  one  of 
the  ions  involved  in  an  electrolytic  dissociation  equi- 
librium by  adding  another  electrolyte  with  a  common 
ion.  The  result  of  this  is  to  repress  the  dissociation 
of  the  first  electrolyte,  that  is,  to  increase  the  concen- 
tration of  the  undissociated  molecules.  If,  now,  the 
solution  is  already  saturated  with  this  first  electrolyte, 
it  cannot  contain  any  more  of  the  undissociated  mole- 
cules; the  consequence  is  that  some  of  the  electrolyte 
separates  out  in  solid  form.  The  law  of  mass  action, 
then,  applied  to  the  dissociation  equilibrium  in  the 
saturated  solution  of  an  electrolyte  AB,  leads  us  to 
expect  that  the  addition  of  another  electrolyte  which 
yields  either  A'  or  B'  as  one  of  its  ions,  will  throw 
some  of  the  compound  AB  out  of  solution ;  in 
other  words,  will  lower  the  solubility  of  AB.  This 
conclusion  is  amply  verified  by  experiment.  If  to  a 
saturated  solution  of  barium  nitrate  we  add  a  little 
concentrated  nitric  acid,  solid  barium  nitrate  is  pre- 
cipitated ;  the  addition  of  a  little  concentrated  solution 
of  either  silver  nitrate  or  sodium  acetate  to  a  saturated 
solution  of  silver  acetate  throws  down  some  of  the 
latter  salt.  The  following  figures  give  a  more  definite 
shape  to  the  results  of  experiment : 1  they  represent 
the  extent  to  which  the  solubility  of  thallous  chloride 
at  25°  is  affected  by  the  presence  of  an  electrolyte  with  a 
common  ion,  namely,  either  thallous  nitrate  or  hydro- 
chloric acid;  all  figures  are  given  in  gram-mols.  per  litre: — 

Solubility  of  Thallous  Chloride. 

Concentration  of  the  In  Presence  of  In  Presence  of 

added  Electrolyte.  T1N03.  HC1. 

0-0  0-0161  0-0161 

0-0283  0-0083  O'OOSJW 

0-0560  0-00571  0'00565 

0-1468  0-00332  0-00316 

The   diminution   in   the  solubility  brought   about   by 

1  See  Noyes,  Zcit.  physical.  Chem.,  1893,  6,  249. 


CHEMICAL  EQUILIBRIUM  269 

increasing  quantities  of  an  electrolyte  with  a  common 
ion  is  very  marked,  and  a  comparison  of  the  figures  in  the 
last  two  columns  shows  that  the  effect  is  pretty  much 
the  same  whether  the  common  ion  is  anion  or  cation, 
provided  the  added  electrolytes  are  dissociated  to  about 
the  same  extent.  On  these  lines  also  we  get  an  in- 
telligible explanation  of  the  practice,  common  in 
analytical  operations,  of  adding  a  slight  excess  of  a 
precipitating  reagent ;  any  slight  solubility  which  the 
precipitate  may  have  is  thereby  reduced. 

What,  it  may  be  asked,  would  be  the  result  of  adding 
to  a  saturated  solution  of  an  electrolyte  another  electro- 
lyte which  has  no  ion  common  with  the  first?  The 
principles  already  laid  down  enable  us  to  deal  with 
this  case.  For  the  addition  of  an  electrolyte  with  no 
common  ion  makes  possible  the  formation  of  two  new 
undissociated  substances,  and  in  proportion  as  these  are 
formed  the  concentrations  of  the  ions  of  the  original 
electrolyte  are  reduced.  In  order  to  maintain  the  con- 
dition c^2  =  const,  some  of  the  undissociated  mole- 
cules of  the  original  electrolyte  dissociate,  thereby 
making  room  for  the  passage  of  fresh  solid  into  solution. 
The  solubility,  therefore,  of  a  sparingly  soluble  electro- 
lyte must  be  increased  in  presence  of  another  which 
has  no  ion  common  with  the  first.  This  conclusion 
also  is  in  harmony  with  observation.1  Benzoic  acid,  for 
instance,  is  more  soluble  in  sodium  acetate  solutions 
than  it  is  in  water,  a  fact  which  is  brought  out  by 
the  figures  quoted  in  the  following  table : — 

Concentration  of  Solubility  of 

Sodium  Acetate.  Benzoic  Acid. 

O'OO  0-0289 

0-0099  0-0370 

0-0198  0-0446 

0-0493  0-0643 

1  See  Noyes  and  Chappin,  Journ.  Amcr.  Chem.  Soc.,  1898,  20,  751; 
Philip,  Journ.  Chem.  Soc.,  1905,  87,  987 ;  1909,  95,  1466. 


270  PHYSICAL  CHEMISTEY 

The  numbers  given  represent  in  all  cases  gram-mole- 
cules per  litre  of  solution.  When  sodium  acetate  is 
added  to  a  saturated  solution  of  benzoic  acid,  the  two 
new  compounds  which  may  be  formed  by  reactions 
between  the  ions  are  sodium  benzoate  and  acetic  acid. 
The  first  of  these  compounds  is  highly  dissociated,  like 
all  salts  of  this  type,  so  that  its  formation  is  respon- 
sible for  the  removal  of  only  a  small  quantity  of  the 
C6H5.COO'  ions.  Acetic  acid,  on  the  other  hand,  is  a 
feebly  dissociated  compound,  and  its  formation  means 
a  relatively  complete  removal  of  the  hydrogen  ions. 
This  leads  to  a  big  disturbance  of  the  equilibrium 
between  benzoic  acid  and  its  ions,  to  the  dissociation 
of  the  benzoic  acid  molecules,  and  to  the  replacement 
of  these  by  fresh  solid  passing  into  solution.  If  sodium 
chloride  were  added  instead  of  sodium  acetate,  the 
effect  on  the  solubility  of  benzoic  acid  would  be  very 
slight  indeed,  because  hydrochloric  acid  is  highly  dis- 
sociated compared  with  acetic  acid.  On  similar  lines 
intelligible  explanations  can  be  given  of  such  facts  as 
that  silver  acetate  is  soluble  in  nitric  acid,  and  that 
magnesium  hydroxide  is  more  soluble  in  solutions  of 
ammonium  chloride  (or  the  chloride  of  any  weak  base) 
than  in  pure  water. 

The  Law  of  Mass  Action  in  Immunochemistry.1— 

Within  recent  years  the  nature  of  the  relationship 
between  toxins  and  antitoxins  has  attracted  much 
attention.  The  work  of  Ehrlich  and  others "  has  shown 
that  the  addition  of  an  antitoxin  to  the  corresponding 
toxin  resembles  generally  the  neutralisation  of  an  acid 
by  an  alkali,  but  the  fact  has  emerged  also  that  the 
amount  of  toxin  neutralised  is  not  proportional  to  the 

1  See  Arrhenius,  Immunochemistry ;  alst^  Michaelis  in  Koranyi  and 
Richter's  Physikalische  Chemie  und  Medizin,  vol.  ii. 


CHEMICAL   EQUILIBRIUM  ,  271 

amount  of  antitoxin  added.  The  process  is  therefore 
not  strictly  analogous  to  the  neutralisation  of  a  strong 
acid  by  a  strong  base,  but  rather  to  that  of  a  weak 
acid  by  a  weak  base.  In  the  latter  case  the  hydrolytic 
dissociation  of  the  salt  interferes  with  the  normal  course 
of  neutralisation,  and  in  a  mixture  containing  equivalent 
quantities  of  a  weak  acid  and  a  weak  base  there  is 
still  free  acid  and  free  base.  These  are  in  reversible 
equilibrium  with  the  salt,  thus:  AB+H2O^HA+BOH. 
To  such  a  reversible  equilibrium  the  law  of  mass  action 
may  be  applied,  and  it  follows  that  by  adding  excess 
of  the  acid  the  concentration  of  the  free  base  is 
diminished,  but  only  gradually. 

The  fact  that  in  a  solution  containing  equivalent 
quantities  of  a  weak  base  and  a  weak  acid  there  is 
free  base  and  free  acid  is  brought  out  by  a  study  of 
the  neutralisation  of  ammonia  by  boric  acid.1  Free 
ammonia  is  a  haamolytic  agent,  that  is,  acts  on  red 
blood  -corpuscles  so  as  to  bring  about  the  escape  of  the 
haemoglobin ;  boric  acid,  on  the  other  hand,  exerts  no 
appreciable  haemolytic  action.  The  gradual  neutralisa- 
tion of  ammonia  by  boric  acid  is  therefore  marked  by 
decreasing  hsemolytic  activity,  and  the  toxicity  (in  relation 
to  red  blood  corpuscles)  of  a  solution  containing  both 
ammonia  and  boric  acid  may  in  fact  be  taken  as  a 
measure  of  the  free  ammonia  which  it  contains.  Since 
the  addition  of  an  exactly  equivalent  quantity, of  hydro- 
chloric acid  .to  sodium  hydroxide  solution  completely 
removes  the  ha3molytic  effect  of  the  latter,  it  might 
perhaps  be  expected  that  the  addition  of  an  equivalent 
quantity  of  boric  acid  to  ammonia  would  give  a  mixture 
which  is  non-toxie  in  regard  to  red  blood  corpuscles. 
This,  however,  is  not  the  case,  as  appears  from  the 

1  See  Arrhenius  and  Madsen,  Zcit.  pliysikal.  Chem.,  1903,  44,  7. 

e 


272  PHYSICAL   CHEMISTRY 

data  recorded  in  the  accompanying  table.     The  figures 

n.  Toxicity. 

0  100 
0-17  85 

0-33  69 

0-67  43 

1-0  26 

1-33  20 

1-67  13 

2-0  10 

in  the  second  column  represent  the  toxicity  (deduced 
from  the  hsemolytic  power)  of  solutions  of  1  equivalent 
of  ammonia,  to  which  n  equivalents  of  boric  acid  have 
been  added.  It  is  evident  that  a  solution  in  which 
there  are  equivalent  quantities  of  ammonia  and  boric 
acid  still  contains  free  ammonia,  and  that  addition  of 
excess  of  boric  acid  only  gradually  reduces  the  con- 
centration of  the  free  base. 

There  is  a  considerable  amount  of  evidence  available 
which  shows  that  in  a  neutral  mixture  of  a  toxin  and 
its  antitoxin  a  certain  proportion  of  each  exists  in  the 
free  state.  There  is,  for  instance,  the  work  done  by 
Craw1  on  the  lysin  obtained  from  cultures  of  Bacillus 
megatherium.  This  lysin  passes  through  a  gelatin  filter, 
whereas  the  corresponding  antilysin  is  kept  back. 
Making  use  of  this  difference  between  the  two  bodies, 
Craw  was  able  to  show  that  both  neutral  mixtures2 
and  those  with  excess  of  antilysin  contain  free  lysin, 
also  that  both  neutral  mixtures  and  those  with  excess 
of  lysin  contain  free  antilysin.  Neutral  mixtures,  there- 
fore, of  lysin  and  antilysin  contain  both  substances  to 
some  extent  in  the  free  state,  and  the  question  arises 
whether  they  are  in  reversible  equilibrium  with  some 
compound  formed  by  the  union  of  lysin  and  antilysin. 

1  Proc.  Roy.  Soc.,  B,  1905,  76,  179. 

2  Mixtures,  that  is,  which  did  not  hasmolyse  in  the  standard  time. 


CHEMICAL  EQUILIBRIUM  273 

On  the  question  of  the  reversibility  of  the  toxin- 
antitoxin  reaction  the  evidence  is  somewhat  conflicting. 
Craw  finds  that  the  reaction  between  megatherium  lysin 
and  antilysin  is  reversible  when  excess  of  antilysin 
is  present,  but,  on  the  other  hand,  the  Danysz  pheno- 
menon may  be  quoted  (see  p.  215).1  Danysz  found 
that  the  toxic  properties  of  a  mixture  of  diphtheria 
toxin  and  antitoxin  depend  on  the  manner  in  which 
they  are  mixed.  Suppose  A  and  T  are  quantities  of 
antitoxin  and  toxin  such  that  when  A  is  added  to  T 
all  at  once  the  mixture  is  innocuous ;  then  it  is  found 
that  if  A  is  added  to  T  at  intervals,  a  portion  at  a 
time,  the  resulting  mixture  is  toxic.  This  observation 
is  difficult  to  reconcile  with  the  view  that  there  is  a 
true  reversible  equilibrium  between  toxin  and  anti- 
toxin.2 Further  arguments  against  the  view  that  the 
toxin-antitoxin  reaction  is  strictly  reversible  have  been 
brought  forward  by  Nernst  and  others.3 

Considerable  difference  of  opinion  exists  also  on  the 
question  how  far  toxins  and  antitoxins  are  in  a  state 
of  true  solution.  Some  regard  them  purely  as  colloids, 
even  suspension  colloids,  and  consider  that  the  relation 
between  them  is  one  of  adsorption  equilibrium.  The 
treatment  of  the  toxin-antitoxin  relationship  from  this 
point  of  view  has  been  already  illustrated  at  the  close 
of  the  previous  chapter  in  reference  to  the  phenomenon 
of  agglutination. 

Arrhenius,  on  the  other  hand,  has  found  that  diphtheria 
toxin  and  antitoxin,  tetanolysin  and  antitetanolysin,  have 
a  definite  power  of  diffusion,  and  may  be  regarded  as 
in  a  state  of  true  solution.  He  considers  that  the  equi- 
librium between  a  toxin  and  its  antitoxin  is  reversible 

1  See  Journ.  Hygiene,  1907,  7,  501. 

2  See,  however,  Arrhenius,  Journ.  Hyyicne,  1908,  8,  1, 

3  Zeit.  Elcktrochem.,  1904,  10,  377,  783. 


274  PHYSICAL   CHEMISTRY 

in  the  ordinary  sense,  and  that  therefore  the  law  of 
mass  action  may  be  applied.  In  various  cases  the 
neutralisation  of  a  toxin  by  its  antitoxin  has  been  in- 
vestigated from  this  point  of  view,  and  the  course  of 
neutralisation'  is  found  to  be  in  harmony  with  an  equi- 
librium formula  similar  to  that  which  represents  the 
neutralisation  of  ammonia  by  boric  acid.  In  the  case, 
for  instance,  of  tetanolysin,  the  following  formula  was 
found  to  apply :  cxc2  =  TTc2,  where  cv  c2,  and  c  are  the 
quantities  of  free  lysin,  free  antilysin,  and  bound  lysin 
respectively,  and  /if=0'115  at  20°.  The  quantity  of  free 
lysin  in  any  mixture  was  deduced  from  its  haemolytic 
power.  How  far  the  experimental  figures  are  in  harmony 
with  the  foregoing  formula  will  be  seen  from  the  follow- 
ing table,  in  which  n  is  the  added  quantity  of  antilysin  :— 

n.                             Ci  found.  c,  calc. 

0  100  100 

0-05  82  82 

0-1  70  66 

0-15  52  52 

0-2  36  38 

0-3  22  23 

0-4  14-2  13-9 

0-5  10-1  10-4 

0-7  6-1  6-3 

1-0  4-0  4-0 

1-3  2-7  2-9 

1-6  2-0  2-5 

2-0  1-8  1-9 

There  can  be  no  doubt  that  there  is  remarkable  agree- 
ment between  the  observed  and  calculated  values  for  the 
quantity  of  free  lysin,  and  the  formula  c^cz  =  Kc2  evidently 
represents  the  actual  numerical  relationship  between  the 
quantities  involved.  On  this  ground  Arrhenius  draws 
the  conclusion  that  the  reaction^-  between  toxin  and 
antitoxin  is  to  be  represented  as  1  mol.  toxin  +  1 


CHEMICAL  EQUILIBRIUM  275 

antitoxin^ 2  mols.  toxin-antitoxin  compound.  In  view, 
however,  of  the  doubts  which  exist  as  to  the  legitimacy 
of  applying  the  law  of  mass  action  to  the  toxin- antitoxin 
reaction,  the  foregoing  conclusion  must  be  accepted  with 
reserve.1 

1  The  discussion  of  Ehrlich's  views  and  the  exposition  of  his  side 
chain  theory  lie  beyond  the  scope  of  this  volume. 


CHAPTER  XIII 

THE  VELOCITY  OF  CHEMICAL  REACTION 

General. — In  the  foregoing  chapter  the  velocity  with 
which  a  reversible  reaction  A+B  ^  C+D  proceeds  to 
its  condition  of  equilibrium  has  been  conceived  as  the 
resultant  of  two  component  velocities,  one  the  velocity 
with  which  A  and  B  react  to  form  0  and  D,  the  other 
the  velocity  with  which  0  and  D  react  to  form  A  and  B. 
At  the  point  of  equilibrium  these  velocities  are  equal, 
the  amount  of  change  resulting  from  the  forward  re- 
action per  unit  of  time  exactly  balancing  the  amount 
of  change  which  results  from  the  back  reaction.  If 
the  reaction  is  such  that  the  equilibrium  position  is 
almost  at  one  extreme,  say,  at  that  represented  by  the 
right-hand  side  of  the  equation  A-\-B^C-\-D,  then 
the  back  reaction  is  negligible  in  comparison  with  the 
forward  reaction  except  when  the  equilibrium  is  nearly 
reached ;  that  is,  the  velocity  of  the  reaction  for  the 
greater  part  of  its  course  is  simply  the  velocity  with 
which  A  and  B  react  to  form  C  and  D.  On  the  basis 
of  the  law  of  mass  action,  therefore,  the  velocity  of 
the  reaction  at  any  moment,  supposing  that  it  takes 
place  in  a  homogeneous  system,  is  proportional  to  the 
product  of  the  molecular  concentrations  of  A  and  B 
at  that  moment.  If  a  and  b  represent  the  molecular 
quantities  of  A  and  B  which  were  mixed  initially,  and 
if  after  an  interval  of  time  t  the  molecular  quantity  of 
C  and  D  formed  is  x,  then  the  velocity  V  of  the 
reaction  at  this  interval  from,  the  start  will  be  given  by 

276 


VELOCITY   OF   CHEMICAL  REACTION     277 

V=k1(a-x)(b  -x).  But  the  velocity  of  the  reaction 
may  be  defined  as  the  rate  at  which  x  is  increasing 

with  the  time, — ^,  as  it  is  put  in  the  language  of  the 
differential  calculus.  The  formula  therefore  which,  on 
the  basis  of  the  law  of  mass  action,  ought  to  represent 
the  rate  of  the  change  A -\-B~Z_  C+D,  when  the  change 
proceeds  until  either  A  or  B  has  practically  disappeared, 

isTt  =  kl(a-xXb-x'). 

Inversion  of  Sucrose:  a  Unimolecular  Reaction. — A 

common  example  of  a  reaction  of  the  type  A-\-B  ^±  C-\-D, 
one  too  which  fulfils  the  condition  that  the  reaction  shall 
proceed  until  either  A  or  B  has  practically  disappeared, 
is  the  inversion  of  sucrose.  The  change  which  occurs 
in  the  inversion  of  sucrose  may  be  represented  as 

^12^22^11  +  H20  =  2C6H1206, 

for  although  the  change  takes  place  with  appreciable 
velocity  only  in  the  presence  of  a  catalytic  agent,  such 
as  hydrochloric  acid,  yet  the  latter  is  found  unaltered 
when  the  reaction  is  over.  Since  the  inversion  is  carried 

out  in  aqueous  solution  the  formula  ~=/£i(&  —  x)(b  —x) 

may  be  simplified,  for  in  this  case  the  water  which 
actually  disappears  in  the  reaction  is  a  very  small 
fraction  of  the  total  water  present ; l  x  may  therefore  be 
neglected  in  comparison  with  b,  and  we  have 

-^  =  ld(a  -  x)b  =  k(a  -  x),  where  k  =  kjj. 
Integration  of  the  equation  ^--  =  k(a  —  x)  leads  to  the 

formula  k  =  ,-  loge  — ^— ,  in  which,  as  already  indicated, 
a  is  the  quantity  of  sucrose  originally  present,  and  a  -  x 

1  Suppose,  for  instance,  that  a  solution  containing  171  grams  of 
sucrose  per  litre  is  considered.  In  1  litre  of  this  solution  there  is 
877  grams  of  water,  whereas  the  quantity  of  water  combining  with 
the  171  grams  of  sucrose  during  inversion  is  only  9  grams 


278  PHYSICAL   CHEMISTRY 

is  the  quantity  still  to  be  inverted  after  an  interval  t 
from  the  start.  Any  method  which  permits  a  relatively 
rapid  determination  of  the  quantity  of  sucrose  in  the 
inverting  solution  at  a  given  time  enables  us  to  test 
the  applicability  of  this  formula,  but  the  only  method 
practically  employed  in  studying  the  rate  of  inversion  of 
sucrose  is  that  which  depends  on  the  use  of  the  polari- 
meter.  It  is  well  known  that  a  solution  of  sucrose  has  a  + 
rotation,  whereas  the  completely  inverted  solution  has 
a  —  rotation ;  further,  the  change  in  rotation  from  the  initial 
angle  a0  to  the  final  angle  a^,  observed  after  inversion 
is  complete,  is  a  measure  of  the  total  quantity  of  sucrose 
undergoing  change.  Similarly,  if  a  is  the  angle  of 
rotation  observed  for  the  solution  after  an  interval  t  from 
the  start,  the  difference  between  a  and  am  is  a  measure 
of  the  sucrose  which  has  still  to  be  inverted  after  time  t. 
If,  then,  a0  -  am  is  taken  as  a  measure  of  a,  a  -  a*  is  a 

measure  of  a  —  x  in  the  same  units :  hence  -—  =  a°    aao> 

a  -x      a~  ax> 

The  velocity  formula  may  therefore  be  altered  to  read 
k  =  -  loge  JL— 2.  The  inversion  may  be  allowed  to  take 

place  in  the  tube  of  the  polarimeter  itself,  provided  that 
a  constant  temperature  is  maintained  by  a  water-jacket. 
It  is  a  matter  of  common  experience  that  the  temperature 
coefficient  of  a  chemical  reaction  is  high,  hence  in  any 
experimental  study  of  the  applicability  of  the  velocity 
formula  care  must  be  taken  to  ensure  a  constant  tem- 
perature. When  a  solution  of  sugar  containing  acid 
is  kept  in  a  suitably  jacketed  polarimeter  tube,  the 
knowledge  of  the  angle  of  rotation  determined  at  definite 
intervals  enables  us  to  follow  the  course  of  the  change 
and  to  evaluate  k  for  each  point.  The  data  in  the 
following  table  show  how  far  jthe  actual  course  of 
inversion  corresponds  with  the  velocity  formula : — 


VELOCITY   OF   CHEMICAL  EE  ACTION    279 

Inversion  of  Sucrose  at  25°  by  0'5N  HCl. 

0                       +25-16° 
56                        16-95° 
116                        10-38° 
176                          5-46° 
236                          1-85° 
371                       -3-28° 
oo                       -8-38° 

n,  —  _      -°10 
a  ~     ao 

0-00218 
0-00218 
0-00219 
0-00219 
0-00221 

It  ought  to  be  noted  that  the  expression  which  has 
been  evaluated  in  the  last  column  is  ^  Iog10  aQ~a<:0  , 

instead  of  ^  loge  — £^  .     But,  obviously,  if  the  values 

of  the  former  expression  are  constant,  the  values  of 
the  latter  must  be  so  also.  The  figures  in  the  last 
column  are  very  satisfactorily  constant,  and  the  mean 
value  0-00219  may  be  taken  as  a  measure  of  the 
velocity  of  inversion  of  sucrose  under  the  conditions 
specified,  viz.  at  25°  and  in  presence  of  0-5N  HCl.  The 
variation  in  the  velocity  coefficient  with  temperature 
and  with  the  concentration  of  the  acid  will  be  dis- 
cussed later. 

Keactions,  such  as  the  inversion  of  sucrose,  in  which 
the  concentration  of  one  substance  only  is  undergoing 
change,  are  known  as  unimolecular  reactions.  The 
course  of  all  changes  of  this  description  is  expressed 

by  the  formula  k  =  ^  log  ^^.-     All  hydrolytic  changes 

which  take  place  in  aqueous  solution  belong  to  this 
categoiy,  as,  for  instance,  the  reaction 

CH3.COOCH3  +  H20  JCH3.COOH  +  CH3OH ; 

under  the  influence  of  an  acid  this  change  goes  com- 
pletely from  left  to  right,  and  the  course  of  the  change 
is  represented  by  the  foregoing  formula. 

The    rate    of   hydrolysis    of   methyl   acetate,    like   the 


280  PHYSICAL   CHEMISTRY 

rate  .of  sugar  inversion,  is  within  certain  limits  pro- 
portional to  the  concentration  of  the  hydrogen  ions 
present.  A  determination,  therefore,  of  the  rate  of 
hydrolysis  of  methyl  acetate  as  influenced  (1)  by  any 
feebly  acid  fluid,  (2)  by  dilute  hydrochloric  acid  con- 
taining a  known  quantity  of  hydrogen  ions,  permits 
the  calculation  of  the  hydrogen  ion  concentration  in 
the  said  fluid.  In  this  way  information  can  be  gained 
which  a  mere  titratioii  cannot  give,  for  by  the  latter 
operation  we  determine  only  the  total  acidity  of  the 
fluid,  and  obtain  no  indication  of  the  ratio  of  ionised 
acid  to  total  acid.  By  a  study,  however,  of  the  in- 
fluence of  the  fluid  in  question  on  the  velocity  of 
hydrolysis  of  methyl  acetate  the  extent  of  the  ionisa- 
tion  is  ascertained.  This  method  has  been  employed, 
for  instance,  in  the  investigation  of  the  acidity  of  the 
contents  of  the  stomach.1 

Further  Discussion  of  the  Formula  for  a  Unimolecular 
Reaction. — The  formula  k  =  -  loge  ^3^,  which  represents 

the  course  of  a  unimolecular  reaction,  has  in  the  fore- 
going pages  been  reached  by  purely  mathematical 
operations.  Although  this  is  in  one  sense  absolutely 
satisfactory,  it  is  worth  while  to  consider  a  little  more 
in  detail  what  is  involved  in  the  formula,  and  to  en- 
deavour to  translate  the  mathematical  expressions  into 
terms  which  may  be  more  capable  of  direct  interpre- 
tation. For  this  purpose  it  will  be  convenient  to  refer 
specially  to  the  inversion  of  sucrose;  any  conclusions 
established  for  this  typical  unimolecular  reaction  may 
be  extended  to  cover  other  reactions  which  belong  to 
the  same  type. 

The  fundamental  formula  for  the  inversion  of  sucrose 

1  See  Moore,  Proc.,  Roy.  Soc.,  B,  1905,  76,  138. 


VELOCITY  OF  "CHEMICAL   REACTION     28] 

is,   as   already   quoted,   ~  =  k(a  -  x),    where    dx    is    the 

amount  of  change  in  the  interval  of  time  dt,  a-x  is 
the  amount  of  unchanged  sugar  at  the  moment,  and 

k  is  a  constant.     If  the  formula  is  written  — —  =  kdt, 

a  —  x 

it  is  evident  that  for  a  given  interval  of  time  the  amount 
of  change  must  be  a  constant  fraction  of  the  un- 
changed sugar  present.  Experimental  work  on  the 
rate  of  inversion  of  sucrose  confirms  this  conclusion, 
as  appears  from  consideration  of  the  data  in  the  follow- 
ing table.1  A  sucrose  solution  containing  17*1  grams 

Time.  a 

0  -1-21 -55° 

15  20-40° 

120  13-75° 

135  12-95° 

225  8-62° 

240  8-02° 

oo  -7-18° 

of  sugar  per  100  cub.  cm.  was  inverted  at  20°  under 
the  influence  of  hydrochloric  acid,  and  the  progress 
of  the  change  was  followed  by  determining  the 
rotation  (a)  of  the  solution  from  time  to  time.  The 
decrease  in  rotation  during  the  first  15  minutes,  namely, 
1'15°,  is  a  measure  of  the  amount  of  change  which 
has  taken  place  during  that  interval.  The  average 
rotation  of  the  solution  for  the  same  interval  of  15 

T  21-55  +  20-40        OA  nrT 

minutes   may   be   taken    as    -     — ^ —   -  =  20'9 /,    and    a 

measure  of  the  mean  amount  of  unchanged  sucrose  pre- 
sent during  this  interval  is  given  by  20'97  +  7'18:=  28-15. 
The  ratio  of  the  amount  of  change  in  the  first  15 
minutes  to  the  unchanged  sucrose  present  may  there- 
fore be  taken  as  -^7—  =  0'041.  If,  now,  the  interval 

Zo  LO 

1  Armstrong  and  Caldwell,  Proc.  Roy.  Soc.,  A,  1905,  74,  199. 


282  PHYSICAL   CHEMISTRY 

between  120  and  135  minutes  is  considered,  the  amount 
of  change  measured  by  the  decrease  of  rotation  which 
is  found  for  that  interval  is  O'SO.  The  average  rotation 
of  the  solution  during  these  15  minutes  may  be  taken 

13-75  +  12-95  -. 

as    -  -  -  =  lo'oo,    and    a    measure    01    the    mean 

amount  of  unchanged  sucrose  present  is  given  by 
13-35  +  7-18  =  20-53.  The  ratio  of  the  amount  of  change 
in  those  15  minutes  to  the  unchanged  sucrose  present 

is  therefore  =  0'039,  practically  the  same  value  as 


for  the  first  15  minutes  of  the  inversion.  Again,  if 
the  data  for  a  still  later  interval  (225-240  minutes) 
are  considered,  the  ratio  of  the  amount  of  change  to 
the  unchanged  sucrose  present  works  out  to  0*039. 
The  experimental  data,  therefore,  are  in  harmony  with 
the  statement  that  in  a  unimolecular  reaction  the  amount 
of  change  in  a  given  short  interval  is  a  constant  fraction 
of  the  unchanged  material  present. 

Another  result  which  can  be  read  out  of  the  formula 
for  the  inversion  of  sucrose  becomes  clear  when   it  is 

written  in  the  form  k  =  ^  loge  —  -  =  ^  loge  ^—  ,  y  repre- 

a 

senting  the  fraction  of  the  sucrose  which  has  undergone 
change  up  to  time  t.  Since  k  is  a  constant  for  this 
reaction  at  a  given  temperature,  it  follows  that  for 
any  selected  value  of  t,  y  must  have  a  definite  value; 
the  fractional  amount  therefore  of  the  sucrose  inverted 
in  a  given  time  is  independent  of  a,  i.e.  independent 
of  the  amount  of  sucrose  initially  present.  The  validity 
of  this  conclusion  may  be  tested  by  comparing  the 
values  of  the  velocity  coefficient  obtained  in  experiments 
carried  out  with  varying  quantities  of  sucrose  :  the 
theory  requires  that  the  velocity  coefficients  so  obtained 
should  be  equal.  How  far  this  is  the  case  will  appear 


VELOCITY  OF   CHEMICAL  KEACTION    283 
from  the  figures  in  the  following  table.1     The  numbers 

Gram-mols.  t  j. 

of  Sucrose.  **' 

0'25  560  504 

0-5  622  510 

075  698  513 

1-0  770  521 

in  the  first  column  represent  the  quantity  of  sugar 
taken,  and  the  numbers  under  /^  in  the  second  column 
are  the  mean  values  of  the  velocity  coefficient  for  each 
experiment,  the  sugar  solution  containing  hydrochloric 
acid  in  each  case  to  the  extent  of  1  gram-molecule 
per  litre.  Instead  of  being  constant,  as  the  theory 
requires,  the  values  of  /^  increase  markedly  as  the 
sucrose  concentration  increases.  It  has,  however,  been 
pointed  out  that  as  the  sucrose  concentration  increases, 
the  amount  of  water  present  in  1  litre  of  sucrose  solution 
diminishes  to  a  considerable  extent ;  the  concentration 
of  the  hydrochloric  acid,  therefore,  which  acts  as  the 
catalytic  agent,  is  not  constant  throughout,  and  hence 
the  values  for  kt  cannot  fairly  be  compared.  If  the 
proportion  of  acid  to  water  is  kept  constant,  that  is, 
if  the  sucrose  and  the  gram-molecule  of  hydrogen 
chloride  are  in  each  case  dissolved  in  1000  grams  of 
water,2  then  the  values  recorded  under  Jc2  are  obtained 
for  the  velocity  coefficient.  The  extent  to  which  these 
values  vary  with  increasing  quantity  of  sucrose  is  com- 
paratively slight,  and  they  may  therefore  be  regarded 
as  confirming  the  statement  that  the  fractional  amount 
of  sucrose  inverted  in  a  given  time  is  independent  of 
the  amount  of  sucrose  originally  present. 

Saponification  of  an  Ester  by  an  Alkali.     A  Bi- 
molecular  Reaction. — When  sodium  hydroxide  is  added 

1  Caldwell,  Proc.  Roy.  Soc.,  A,  1906,  78,  287. 

2  For  this  method  of  preparing  solutions,  see  p.  48. 


284  PHYSICAL   CHEMISTRY 

to  a  solution  of  ethyl  acetate,  the  ester  is  gradually 
decomposed  into  sodium  acetate  and  ethyl  alcohol.  The 
progress  of  the  decomposition  is  marked  by  the  decreasing 
alkalinity  of  the  solution,  and  therefore  by  extracting 
a  measured  portion  from  time  to  time,  and  titrating 
with  standard  acid,  the  velocity  of  the  reaction  can 
be  quantitatively  studied.  The  saponification  of  the 
ester  may  be  represented  by  the  equation 

CH3.COOC2H5  +NaOH  =  CH3.COONa + C2H5OH, 
from  which  it  will  be   seen  that  in  this  case  the  con- 
centrations   of   two  substances    undergo    change   during 
the  reaction.     The  law   of  mass  action   applied  to  this 

case  leads  to  the  formula  -^  =  k(a -x)(b -x),   where  a 

and  b  are  the  initial  quantities  of  ester  and  alkali, 
and  x  is  the  quantity  of  sodium  acetate  produced  after 
an  interval  t  from  the  start.  If  this  equation  is  inte- 
grated, we  find  the  velocitv  constant  k  =  -, — ^-.  log1,,  4? — -4 

J  (a-b)t      De  a(b  —  x)' 

The  mathematical  expression  which  represents  the 
course  of  the  reaction  becomes  simpler  if  the  ester 
and  alkali  are  taken  in  equivalent  quantities,  i.e.  if  a  =  b. 

In  this  case  -j?  =  k(a  -  x)2,  the  integration  of  which  gives 

the    formula    k  = ,-  —r— \-      How   far   the   facts   are   in 
i  a(a-x) 

harmony  with  this  formula  may  be  seen  from  the 
figures  in  the  following  table.1  The  solution  used  was  -r 

in  relation  both  to  ester  and  sodium  hydroxide,  and 
during  the  reaction  the  mixture  was  kept  at  24' 7°. 
The  figures  recorded  under  a  -  x  are  the  volumes  of 
a  standard  hydrochloric  acid  required  to  neutralise 
exactly  10  cub.  cm.  of  the  reaction  mixture. 

J  Arrhenius,  Zeit.  physikal.  Chem.,  1887,  1,  110. 


VELOCITY   OF   CHEMICAL  KEACTION     285 


0  8-04 

4  5-30  0-129 

6  4-58  0-126 

8  3'91  0-132 

10  3-51  0-129 

12  3-12  0-131 

15  2-74  0-129 

20  2-22  0-131 

The  numbers  given  in  the  last  column  for  ka  are  very 
satisfactorily  constant,  and  confirm  the  application  of 
the  law  of  mass  action  to  a  bimolecular  reaction. 

As  indicated  on  p.  168,  the  rate  of  inversion  of  sucrose 
and  the  rate  of  saponification  of  an  ester  may  be  utilised 
in  ascertaining  the  concentration  of  hydrogen  or  hydroxyl 
ions  respectively  in  any  solution.  It  must,  however, 
be  borne  in  mind  that  there  is  an  essential  difference 
between  the  two  reactions.  In  the  saponification  of 
an  ester  by  an  alkali,  the  alkalinity  of  the  reaction 
mixture  diminishes  as  the  reaction  proceeds,  i.e.  the 
hydroxyl  ions  disappear.  In  the  inversion  of  sucrose, 
on  the  other  hand,  the  acid  present  does  not  enter 
into  the  products  of  the  reaction,  and  the  quantity  of 
the  acid  or,  in  other  words,  the  concentration  of  the 
hydrogen  ions  remains  the  same  throughout  the  course 
of  the  change.  The  influence  of  acids  in  promoting 
the  inversion  of  sucrose  is  an  example  of  catalytic 
action,  the  general  characteristics  of  which  must  be 
considered  in  some  detail. 

Catalysis.  —  It  is  a  well-known  fact  that  a  chemical 
change  which  of  itself  proceeds  with  extreme  slowness 
may  be  greatly  accelerated  in  presence  of  some  apparently 
foreign  substance,  the  other  conditions  being  unaltered. 
The  amount  of  this  foreign  substance  may  be  extremely 
small,  it  may  not  take  any  obvious  part  in  the  chemical 
change,  it  may  be  quantitatively  recoverable  at  the  end 


286  PHYSICAL   CHEMISTKY 

of  the  change,  and  yet  the  rate  of  the  chemical  reaction 
may  be  markedly  altered.  This  phenomenon  has  been 
known  for  a  long  time,  and  is  familiar  to  the  chemist  as 
'catalysis.'  It  is  of  the  greatest  importance  in  relation 
to  the  chemical  changes  which  take  place  in  the  living 
organism,  for  there  we  find  reactions  occurring  easily 
and  smoothly,  which,  apart  from  the  organism,  are  ex- 
ceedingly sluggish  and  difficult  to  bring  about.  The 
'  catalytic  agents  '  or  '  catalysts  '  which  promote  the  pro- 
cesses of  metabolism  in  the  living  organism  belong  to 
the  class  of  enzymes,  and  it  will  presently  appear  that 
from  the  quantitative  as  well  as  the  qualitative  point 
of  view  there  is  a  close  analogy  between  enzymes  and 
inorganic  catalysts. 

A  quantitative  study  of  catalysis  is  possible  only  on 
the  basis  of  the  law  of  mass  action.  In  the  velocity 
coefficient,  as  already  explained  for  the  inversion  of 
sucrose,  we  have  a  quantitative  expression  for  the  rate 
of  a  chemical  change  under  given  conditions.  For  a 
given  reaction,  therefore,  which  is  catalytically  accelerated, 
the  value  of  the  velocity  coefficient  at  a  given  temperature 
is  a  measure  of  the  efficiency  of  the  catalyst,  and  by 
comparing  the  values  obtained  for  the  velocity  coefficient  in 
different  experiments  one  can  ascertain  how  the  efficiency 
of  the  catalyst  varies  with  the  conditions  under  which  it 
works,  and  how  the  efficiency  of  one  catalyst  compares 
with  that  of  another  working  under  the  same  conditions. 

Characteristics  of  Inorganic  Catalysts. — One  of  the 

most  striking  features  about  a  catalyst  is  that  its  quantity 
may  be  so  minute  compared  with  the  quantities  of  the 
main  reacting  substances.  An  illustration  of  this  is 
furnished  by  the  influence  of  molybdic  acid  on  the  rate 
of  the  reaction  between  hydrogen  peroxide  and  hydriodic 
acid.  Erode  l  has  shown  that  the^velocity  of  interaction 

1  Zeit.  physikal.  Chem.,  1901,  37,  257, 


VELOCITY   OF  CHEMICAL  EEACTION     287 

between  these  substances  in  ^  solution  is  more  than 

doubled  by  the  addition  of  molybdic  acid,  even  in  the 
proportion  of  1  molecule  molybdic  acid  to  1  million  litres 
of  solution. 

Another  point  which  has  been  established  by  the 
quantitative  study  of  inorganic  catalysts  is  that,  as  a 
rule,  the  activity  of  the  catalyst  at  the  end  of  the  re- 
action which  it  has  accelerated  is  unimpaired.  In  this 
connection  reference  may  be  made  again  to  the  fact  that 
the  acid  used  to  effect  the  inversion  of  sucrose  does  not 
appear  in  the  products  of  the  reaction,  and  is  present 
in  undiminished  quantity  when  the  inversion  is  complete. 
Another  illustration  of  the  same  principle  is  furnished  by 
the  behaviour  of  colloidal  platinum  in  promoting  the 
union  of  hydrogen  and  oxygen.  In  the  course  of  some 
experiments  made  by  Bredig,1  it  was  found  that  when 
electrolytic  gas  is  shaken  with  a  colloidal  solution  of 
platinum  at  the  ordinary  temperature,  there  is  a  fairly 
rapid  decrease  in  volume  owing  to  the  union  of  hydrogen 
and  oxygen.  In  one  case  where  2*5  cub.  cm.  of  a 
colloidal  platinum  solution  (containing  O17  milligram 
platinum)  was  shaken  with  electrolytic  gas,  the  results 
recorded  in  the  following  table  were  obtained  : — 

Time  in  Decrease  in  the  Rate  of  Decrease  in 

Minutes.  Volume  of  Gas.  cub.  cm.  per  Mih. 

10  17'8  cub.  cm.  1'78 

20  35-8       „  1-80 

30  54-8       „  1-90 

40  72-4       „  1-76 

50  90-2       „  1-78 

The  average  of  the  figures  in  the  last  column  is  a 
measure  of  the  catalytic  efficiency  of  the  colloidal  platinum 
in  the  early  stages  of  its  activity.  The  same  colloidal 
platinum  was  shaken  intermittently  during  fourteen  days 
with  electrolytic  gas,  about  10  litres  of  which  disappeared 

1  Zeit.  physikal.  Chem.,  1899,  31,  258 ;  see  also  Ernst,  ibid.,  1901,  37,  448. 

T 


288  PHYSICAL   CHEMISTEY 

in  this  time  under  the  influence  of  the  catalyst.  The 
actual  rate  of  disappearance  of  the  gas  at  the  end  of 
the  fourteen  days  was  then  definitely  measured,  with  the 
following  results : — 

Time  in  Decrease  in  the  Rate  of  Decrease  in 

Minutes.  Volume  of  Gas.  cub.  cm.  per  Min. 

10  20-2  cub.  cm.  2'02 

20  38-9       „  1-87 

30  58-4       „  1-95 

40  78-1       „  1-97 

50  98-2       „  2-01 

The  average  of  the  figures  in  the  last  column  is  a 
measure  of  the  catalytic  efficiency  of  the  colloidal  platinum 
after  it  has  exerted  its  activity  for  a  considerable  period. 
It  is  obvious  that  the  efficiency  is  unimpaired  ;  the  aver- 
age rate  of  decrease  in  the  volume  of  the  electrolytic  gas 
is  even  slightly  greater  at  the  end  than  at  the  beginning. 

So  far,  we  have  conceived  a  catalyst  as  a  substance 
which  merely  accelerates  a  chemical  reaction,  and  does 
not  appear  in  the  products  of  the  reaction.  If  this 
is  so,  the  final  state  of  the  reactive  system  must  be 
independent  of  the  catalyst ;  the  state  of  equilibrium 
finally  reached  between  the  reacting  substances  must  be 
the  same  whether  the  catalyst  has  been  present  or  not. 
In  other  words,  the  catalyst  influences  only  the  rate  at 
which  the  condition  of  equilibrium  is  reached,  not  the 
position  of  equilibrium  itself.  The  validity  of  this  con- 
clusion can  be  tested  more  suitably  in  connection  with  a 
reversible  reaction,  for  in  such  a  case  the  position  of 
equilibrium  is  defined  by  the  value  of  the  equilibrium 
constant.  As  already  shown,  the  equilibrium  constant 

for  a  reversible  reaction  is  equal  to  the  ratio  -~y  where  ^ 

is  the  velocity  coefficient  of  the  forward  reaction,  and 
kz  is  that  of  the  back  reaction.  If,  then,  the  position 
of  equilibrium  is  not  affected  by  the  presence  of  a  catalyst, 


VELOCITY   OF  CHEMICAL  REACTION     289 

it  follows  that  the  forward  and  the  back  reactions  must 
be  accelerated  in  the  same  proportion.  This  has  been 
shown  to  be  actually  the  case  in  connection  with  the 
catalytic  action  of  acids  on  the  velocities  of  esterification 
and  hydrolysis  of  an  ester. 

That  the  position  of  equilibrium  for  a  reversible 
reaction  is  independent  of  the  nature  and  amount  of 
catalyst  which  has  been  used  to  accelerate  the  estab- 
lishment of  equilibrium  is  shown  clearly  by  Turbaba's 
study  l  of  the  relationship  between  aldehyde  —  CH3.CHO  — 
and  paraldehyde  —  (CH3.CHO)3.  The  equilibrium  mixture 
of  these  two  substances  at  50'5°  contains  33'9  per  cent. 
aldehyde  and  66*1  per  cent,  paraldehyde.  The  conversion 
of  paraldehyde  into  the  equilibrium  mixture  is  accom- 
panied by  an  expansion,  and  the  course  of  the  change 
may  therefore  be  followed  in  a  dilatometer.  Various 
substances  in  varying  amount  may  be  employed  to 
accelerate  the  change,  but  the  difference  between  the 
initial  and  the  equilibrium  volumes,  as  shown  by  the 
figures  below,  is  the  same  in  all  cases  ;  that  is,  the 
position  of  equilibrium  is  independent  of  the  nature 
and  amount  of  the  catalyst  :  — 


P-t-lvof 
Catalyst. 


Per  Cent.  Percentage  Increase 

Catalyst.  of  Volume. 


Sulphur  dioxide     .     .     .  0'08  8'20 

„  ...  0-07-  8-34 

„  ...  0-002  8-19 

Zinc  sulphate    .     .     ,     .  2'7  8'13 

Hydrochloric  acid  .     .     .  0'13  8'13 

Oxalic  acid    .....  0-52  8'27 

Phosphoric  acid     .     .     .  0'54  8'10 

Another  point  of  great  interest  is  the  relationship 
between  the  value  of  the  velocity  coefficient  for  a  given 
reaction  at  a  given  temperature  and  the  concentration 
of  the  catalyst.  In  a  great  many  cases  the  relation- 

1  See  Zeit.  physical.  Chem.,  1901,  38,  505. 


290  PHYSICAL   CHEMISTRY 

ship  is  a  linear  one,  that  is,  the  velocity  coefficient  is 
directly  proportional  to  the  concentration  of  the  catalyst. 
The  rate  of  inversion  of  sucrose  by  acids,  for  instance, 
is  proportional  to  the  concentration  of  the  hydrogen 
ions,  provided  that  this  concentration  is  low,  and  on 
the  basis  of  this  proportionality  it  is  possible  to  calculate 
the  velocity  of  inversion  by  dilute  acetic  acid  from 
the  velocity  observed  with  dilute  hydrochloric  acid. 
Again,  the  acceleration  of  the  reaction  between  hydriodic 
acid  and  hydrogen  peroxide  by  molybdic  acid  is  propor- 
tional to  the  concentration  of  the  latter.1 

In  other  cases  the  relationship  between  reaction 
velocity  and  concentration  of  catalyst  is  not  a  linear 
one.  The  influence  of  colloidal  platinum  in  promoting 
the  decomposition  of  hydrogen  peroxide  is  a  case  in 
point.2  The  course  of  this  reaction,  it  may  be  explained, 
is  easily  followed  by  extracting  a  definite  volume  of  the 
reaction  mixture  from  time  to  time  and  titrating  with 
a  dilute  solution  of  potassium  permanganate.  The  volume 
of  permanganate  required  for  each  extract  is  a  measure 
of  the  undecomposed  hydrogen  peroxide  present  in  the 
reaction  mixture  at  the  time  of  the  extraction.  For 
a  given  temperature  and  a  given  concentration  of 
colloidal  platinum  the  course  of  the  decomposition  is 
represented  by  the  formula  for  a  ummolecular  reaction ; 
this  appears  from  the  figures  in  the  accompanying  table, 

(niin.  a-x.  k. 

0  22-3 

10  13-6  0-022 

20  8'05  0-022 

30  4-6  0-023 

35  2'8  0-022 

where  the  numbers  under  a  —  x  represent  cub.  cm.  of 
permanganate  required  for  a  given  volume  of  reaction 

1  Erode,  loc.  tit. 

8  See  Bredig  and  von  Berneck,  Zeit.  physikal.  Chem.,  1899,  31,  258. 


VELOCITY   OF   CHEMICAL   EEACTION     291 

mixture,  and  those  under  k  are  the  values  of  the  velocity 
coefficient  calculated  for  a  unimolecular  reaction.  The 
mean  value  obtained  for  k  in  different  experiments 
varies  with  the  concentration  of  the  platinum  in  the 
manner  shown  by  the  following  figures.  From  these 


Platinum 
Concentration. 


k. 


21  x  10-6  0-072 

10-5  x  10 -6  0-024 

5'2xlO-6  0-0084 

2-6xlO-6  0-0027 

it  appears  that  when  the  concentration  of  the  catalyst 
is  doubled,  the  velocity  of  decomposition  is  trebled. 

Enzymes  as  Catalysts.1 — In  many  respects  enzymes 
resemble  inorganic  catalysts.  To  begin  with,  there 
is  the  same  striking  contrast  between  the  small 
quantity  of  the  enzyme  and  the  extent  of  the 
chemical  change  which  it  brings  about.  O'Sullivan 
and  Tompson 2  refer  to  a  sample  of  invertase  which 
had  induced  the  inversion  of  one  hundred  thousand 
times  its  own  weight  of  sucrose  and  was  still  active. 
Senter,  in  the  course  of  experiments  on  hsemase,3  an 
enzyme  present  in  the  blood,  found  that  when  100 
cub.  cm.  of  a  solution  of  blood  (obtained  by  adding 
1  cub.  cm.  of  blood  to  1000  cub.  cm.  of  water)  are 
mixed  with  100  cub.  cm.  of  a  hundredth  molar  solution 
of  hydrogen  peroxide,  the  whole  of  the  latter  is  de- 
composed in  5  minutes,  although  the  solution  without 
any  enzyme  exhibits  no  appreciable  decomposition  in 
3 2  hours. 

Enzymes  resemble  inorganic  catalysts  also  in  that, 
where  the  reaction  involved  is  a  reversible  one,  they 

1  For  a  detailed  discussion  of  this  subject  see  The  Nature  of  Enzyme 
Action,  by  W.  M.  Bayliss. 

2  Journ.  Chem.  Soc.,  1890,  57,  834. 

3  Zeit.  physikal.  Chem.,  1903,  44  257. 


292  PHYSICAL   CHEMISTRY 

promote  both  the  direct  and  the  reverse  changes.  An 
instance  of  this  is  furnished  by  the  action  of  lipase 
on  the  esters  of  the  lower  fatty  acids.  If  this  enzyme 
is  allowed  to  act  on  ethyl  butyrate  in  presence  of 
water,  partial  hydrolysis  into  butyric  acid  and  ethyl 
alcohol  takes  place ;  while  if  it  is  allowed  to  act  on  an 
aqueous  mixture  of  butyric  acid  and  ethyl  alcohol, 
a  certain  quantity  of  the  ester  is  formed.1  The  action 
of  an  enzyme,  however,  on  the  products  of  a  reaction 
may  not  be  strictly  the  reverse  of  its  effect  on  the 
forward  reaction,  for  it  has  been  found2  that  maltase, 
the  enzyme  which  hydrolyses  maltose  into  dextrose, 
exerts  a  synthetic  action  on  dextrose,  producing  not 
maltose,  but  ^so-maltose. 

In  certain  cases  the  course  of  a  reaction  induced  by 
an  enzyme  is  in  harmony  with  the  law  of  mass  action. 
The  decomposition  of  hydrogen  peroxide  under  the 
influence  of  haemase3  may  be  taken  as  an  example 
of  this.  The  course  of  the  decomposition  is  followed 
in  the  same  way  as  already  described  for  the  catalysis 
of  hydrogen  peroxide  by  colloidal  platinum ;  that  is, 
a  definite  volume  of  the  reaction  mixture  is  taken  out 
from  time  to  time  and  titrated  with  dilute  potassium 
permanganate  solution.  That  the  course  of  the  change 
is  in  harmony  with  the  law  of  mass  action  is  shown 


by 

the   following 

table,   the   figures 

under    a  -  x   re- 

t  (min.). 

a—x. 

k. 

0 

ll'O 

&i 

8-7 

0-0194 

10 

7-4 

0-0172 

20 

4-8 

0-0180 

30 

3-0 

0-0188 

50 

1-3 

0-0185 

1  Kastle  and  Loevenhart,  Amer.  Chem.  Journ.,  1900,  24,  491. 

2  Croft  Hill,  Journ.  Chem.  Soc.,  1898,  73,  Q34  ;  1903,  83,  578  ;  Emmer- 
ling,  Ber.,  1901, 34,  600,  2206, 3810  ;  Armstrong,  Proc.  Roy.  Soc.,  B,  1905, 
76,  592. 

3  Senter,  loc.  cit. 


VELOCITY   OF   CHEMICAL  REACTION     293 

presenting  the  volume  of  dilute  permanganate  solution 
required  for  25  cub.  cm.  of  the  reaction  mixture,  and 
those  under  k  being  the  values  of  the  velocity  coefficient 
calculated  for  a  unimolecular  reaction.  The  initial  con- 
centration of  the  hydrogen  peroxide  was  in  this  case 
TVtffch  molar,  and  the  experiments  were  carried  out  at 
0°  C.  The  constancy  of  the  numbers  in  the  last  column 
shows  that  the  catalysis  of  hsemase  follows  the  course 
of  a  unimolecular  reaction.  Further,  it  was  found  by 
Senter  that,  for  hydrogen  peroxide  solutions  between 
^-J^th  and  I0100th  molar  concentration,  the  value  of 
the  velocity  coefficient  is  independent  of  the  initial 
concentration  of  the  hydrogen  peroxide ;  this  also  sup- 
ports the  view  that  the  action  of  haemase  on  hydrogen 
peroxide  is  in  harmony  with  the  law  of  mass  action 
(see  p,  282).  It  appears  too  that,  at  least  in  very  dilute 
solutions  of  hydrogen  peroxide,  the  velocity  of  decom- 
position is  proportional  to  the  concentration  of  the 
enzyme. 

In  many  respects  there  is  a  close  parallelism  between 
the  decomposition  of  hydrogen  peroxide  by  colloidal 
platinum  and  the  decomposition  of  the  same  substance 
under  the  influence  of  haemase.  This  parallelism  ex- 
tends also  to  the  effect  of  certain  'poisons'  in  paralys- 
ing the  activity  of  the  two  catalysts,1  so  much  so  that 
Bredig  has  described  colloidal  platinum  as  an  'inor- 
ganic ferment.' 

The  catalysis  of  hydrogen  peroxide  by  hasmase  has 
been  referred  to  as  a  case  in  which  enzyme  action 
conforms  to  the  law  of  mass  action,  and  in  which  the 
enzyme  behaves  very  similarly  to  an  inorganic  catalyst. 
The  close  study,  however,  of  many  other  cases  has 
shown  that  very  frequently,  owing  to  the  operation  of 

1  Bredig  and  von  Berneck,  Zeit.  physikal.  Chem.,  1899,  31,  258; 
Senter,  loc.  cit.,  and  Proc.  Roy.  Soc.,  1905,  74,  201. 


294  PHYSICAL   CHEMISTRY 

various  factors,  the  course  of  a  reaction  which  takes 
place  under  the  influence  of  an  enzyme  deviates  con- 
siderably from  what  we  should  expect  on  the  basis 
of  the  law  of  mass  action.  A  brief  discussion  of  some 
of  these  factors  may  be  found  useful. 

Some  Peculiarities  of  Enzyme  Action. — As  an  in- 
stance of  an  enzyme  reaction  deviating  from  the  course 
marked  out  by  the  law  of  mass  action,  the  inversion 
of  sucrose  by  invertase  may  be  quoted.  This  change  has 
been  studied  quantitatively  by  A.  J.  Brown,1  and  the 
following  table  embodies  the  results  of  one  of  his  ex- 
periments. In  this  particular  case  25  cub.  cm.  of  in- 
vertase solution  were  added  to  500  cub.  cm.  of  a  9 '48 
per  cent,  sucrose  solution,  and  the  mixture  was  kept 
at  30°.  Portions  were  extracted  from  time  to  time, 
and  from  the  observed  rotation  for  each  sample  the 
extent  to  which  inversion  had  proceeded  at  the  time 
of  extraction  was  deduced ;  the  figures  under  x  repre- 
sent the  fraction  of  the  total  sucrose  which  had  under- 
gone inversion  by  time  t.  The  numbers  in  the  last 
column,  instead  of  being  constant,  as  they  ought  to 
be  if  the  inversion  proceeds  in  conformity  with  the 
law  of  mass  action,  exhibit  a  marked  and  regular 
Increase. 

t  rain.  x.  *  log  JL. 

30  0-265  0-00445 

64  0-509  0-00483 

120  0-794  0-00571 

180  0-945  0-00698 

240  0-983  0-00737 

The  departure  from  the  law  of  mass  action  becomes 
still  clearer  when  experiments  are  made  in  which  a 

1  Journ.  Chem.  Soc.,  1902,  81,  373.  See  also  Henri,  Zeit.  physikal 
Chem.,  1901,  39,  194. 


VELOCITY   OF   CHEMICAL  REACTION     295 

constant  amount  of  invertase  is  allowed  to  act  for 
a  given  time  on  varying  amounts  of  sucrose  in  a 
constant  volume  of  solution.  According  to  the  law 
of  mass  action,  the  fraction  of  the  sucrose  inverted  in 
the  given  time  ought  to  be  the  same  in  all  cases, 
independent,  that  is,  of  the  initial  quantity  of  sucrose 
present.  How  far  this  requirement  of  the  law  of  mass 
action  is  fulfilled  will  be  seen  from  the  accompanying 
table :— 

Grams  Sucrose  Grams  Sucrose  Fraction  of  Sucrose 

per  100  cub.  cm.  Inverted  in  60  min.          Inverted  in  60  min. 

4-89  1-230  0-252 

9-85  1-355  0-138 

19-91  1-355  0-068 

29-96  1-235  0'041 

It  is  clear  that  the  enzyme,  instead  of  inverting 
a  constant  fraction,  has  inverted  an  approximately  con- 
stant weight  of  sucrose  in  the  given  time.  On  the  other 
hand,  if  the  quantity  of  sucrose  is  relatively  much 
smaller  than  in  the  cases  recorded  in  the  foregoing 
table  the  law  of  mass  action  is  fulfilled,  in  that  the 
weight  of  sucrose  inverted  in  a  given  time  is  always 
the  same  fraction  of  the  weight  taken  initially.  This 
appears  from  the  following  figures : — 

Grams  Sucrose  Grams  Sucrose 

per  100  cub.  cm.  Inverted  in  60  min. 

1-0  0-249 

0-5  0-129 

0-25  0-060 

Other  cases  in  which  it  has  been  found  that  the 
amount  of  change  induced  by  an  enzyme  is,  for  at  least 
a  portion  of  the  change,  a  linear  function  of  the  time, 
are  the  hydrolysis  of  starch  by  diastase,1  and  the 
hydrolysis  of  milk  sugar  by  lactase.2 

1  H.  T.  Brown  and  Glendinning,  Journ.  Chem.  Soc.,  1902,  81,  388. 

2  E.  F  Armstrong,  Proc.  Roy.  Soc.,  1904,  73,  500. 


296 


PHYSICAL   CHEMISTRY 


In  connection  with  the  former  of  these  cases  it  has 
been  shown  that  it  is  only  the  earlier  portion  of  the 
time-curve  which  is  linear,  the  later  portion  being 
logarithmic  in  character.  This  is  proved  by  calculat- 
ing the  velocity  coefficient  k  =  -  log  =— -  (1)  for  each 

observation  from  the  start  of  the  reaction,  (2)  for 
each  observation  after  the  linear  portion  has  been 
passed,  a  new  starting  point  being  chosen.  A  com- 
parison of  two  sets  of  values  of  k  obtained  in  this 
manner  is  given  in  the  following  table,  which  refers 
to  the  hydrolysis  of  a  3  per  cent,  starch  solution  by 
malt  extract  at  51°-52°  :— 


Time  (min.). 

10 

20 

30 

40 

50 

60 

70 

80 

90 
100 
110 
120 
130 


k. 

Time  in  min.  from 
new  Starting  Point. 

0-00498 

0-00553 

0-00590 

0-00620 

0 

0-00650 

10 

0-00690 

20 

0-00706 

30 

0-00728 

40 

0-00730 

50 

OO0732 

60 

000749 

70 

0-00762 

80 

0-00779 

90 

0-00842 
0-00831 
0-00821 
0-00837 
0-00818 
0-00807 
0-00822 
0-00840 
0-00855 


It  will  be  seen  that  the  values  of  k  in  the  second  column 
are  far  from  constant,  and  yet  if  the  first  portion  of  the 
change  is  left  out  of  account,  practically  constant  values 
for  the  velocity  coefficient  are  obtained.  It  is  permis- 
sible to  draw  the  conclusion  that  the  later  portion  of  the 
change  conforms  to  the  law  of  mass-action. 

From  the  foregoing  it  appears  that  it  is  only  when  the 


VELOCITY  OF   CHEMICAL  KEACTION     297 

amount  of  enzyme  is  relatively  small  compared  with  the 
amount  of  carbohydrate  that  a  linear  relationship  between 
the  time  and  the  amount  of  change  is  observed.  To 
regard  the  occurrence  of  this  linear  relationship,  however, 
as  something  peculiar  to  enzymes  is  scarcely  correct,  for 
it  has  subsequently  been  found  that  a  similar  feature, 
if  less  distinct,  characterises  the  hydrolysis  of  sucrose 
by  very  dilute  acid.1  When  sucrose  solutions  contain- 
ing 171  and  342  grams  per  litre  are  inverted  at  40°  by 

"N" 

^-r  HC1,  the  values  calculated  for  the  velocity  coefficient 

oOO 

increase  during  the  first  portion  of  the  change  and  then 
remain  constant.  In  this  respect,  therefore,  there  is 
a  close  parallelism  between  acid  and  enzyme  action: 
in  both  cases,  when  the  proportion  of  catalyst  is 
relatively  small,  the  amount  of  change  is  to  begin  with 
approximately  a  linear  function,  and  subsequently  a 
logarithmic  function,  of  the  time. 

Another  peculiarity  about  enzyme  action  which  has 
been  observed  frequently,  is  that  the  activity  of  the  enzyme 
does  not  remain  constant  throughout  the  whole  course  of 
the  change  which  it  induces.  Tammann,2  for  instance, 
found  that  in  the  hydrolysis  of  amygdalin  by  emulsin 
the  change  is  incomplete.  The  failure  of  the  enzyme 
to  effect  complete  hydrolysis  might  be  attributed  to 
the  really  reversible  character  of  the  process,  but  this 
view  is  untenable,  for  if  more  emulsin  is  added  to  a 
mixture  in  which  hydrolysis  has  come  to  a  standstill, 
the  reaction  proceeds  further.  This  shows  clearly  that 
the  equilibrium  reached  when  emulsin  acts  on  amygdalin 
is  not  one  which  is  independent  of  the  enzyme,  as  would 
be  the  case  if  the  emulsin  behaved  like  an  inorganic 
catalyst.  The  natural  conclusion  is  that  the  emulsin 

1  Armstrong  and  Caldwell,  Proc.  Hoy.  Soc.,  1905,  74,  195. 

2  Zeit.  physiol.  Chem.,  1892,  16,  271. 


298  PHYSICAL   CHEMISTRY 

must  be  put  out  of  action  in  some  way  by  the  pro- 
ducts of  hydrolysis — a  view  which  finds  support  in 
the  fact  that  the  action  of  emulsin  on  amygdalin  is 
inhibited  by  the  initial  addition  of  benzaldehyde  or 
hydrocyanic  acid.  This  check  to  the  activity  of  the 
enzyme  cannot,  however,  be  due  to  its  destruction,  for 
when  the  products  of  hydrolysis  present  in  an  equili- 
brium mixture  are  removed,  the  splitting  up  of  the 
amygdalin  sets  in  again. 

The  influence  of  the  products  of  change  on  the  activity 
of  the  enzyme  which  induces  the  change  is  apparent 
also  in  the  values  which  are  found  for  the  velocity 
coefficient  in  the  hydrolysis  of  milk  sugar  by  lactase.1  In 
the  accompanying  table  t  gives  the  time  in  hours  from 

t.                      x.  k. 

1  137  0-0640 

2  22-1  0-0543 

3  27-2  0-0460 
5  30-0  0-0310 

24  51-0  0-0129 

the  start,  x  is  the  percentage  of  sugar  hydrolysed  up 
to  time  t,  and  k  is  the  velocity  coefficient  calculated  by 
the  formula  for  a  unimolecular  reaction  ;  the  solution 
contained  initially  5  grams  milk  sugar  in  100  cub.  cm. 
In  contrast  to  the  case  of  the  inversion  of  sucrose  by 
invertase  (see  p.  294),  the  values  of  k  in  this  case 
decrease  as  the  hydrolysis  proceeds,  a  result  that  is 
attributed  to  the  increasing  concentration  of  the  pro- 
ducts of  hydrolysis.  It  can  indeed  be  shown  that  the 
initial  addition  of  galactose  materially  reduces  the  rate 
of  hydrolysis  of  milk  sugar  by  lactase,  while  glucose 
and  fructose  are  practically  without  effect.  This  appears 
from  the  following  table,  the  figures  in  which,  apart 
from  the  first  column,  represent  the  percentages  of 

1  Armstrong,  Proc.  Roy.  Soc.,  1904,  73,  500. 


VELOCITY   OF   CHEMICAL  EEACTION     299 

milk  sugar  hydrolysed ;  the  concentration  of  milk  sugar 
was  in  each  case  5  grams  per  100  cub.  cm. : — 

Time  in  Milk  Su^ar  Milk  Sugar  Milk  Sugar  Milk  Sugar 

w™,'  +5  grams  +5  grams  +5  grams 

Hour8'  Fructose.  Galactose.  Glucose. 

4  18-0  18-0  16-0  17-6 

22  59-2  59-6  47'4  59'6 

28  65-6  65-4  52-0  65  '4 

69  81-4  80-2  61-6  78-4 

The  retarding  influence  of  the  products  of  change  is 
therefore  a  specific  influence,  depending  on  some  special 
relationship  between  the  enzyme  and  the  particular 
hexose  which  exerts  the  retarding  effect.  Further,  the 
activity  of  the  enzyme,  according  to  the  investigations 
of  Fischer  and  others,1  is  determined  by  the  degree  of 
similarity  in  the  configuration  of  enzyme  and  substrate 
(that  is,  the  substance  undergoing  change  under  the 
influence  of  the  enzyme).  It  is  interesting  to  note,  on 
the  other  hand,  that  the  hydrolysis  of  milk  sugar  by 
hydrochloric  acid  is  accelerated  by  the  addition  of  glucose 
or  galactose ;  the  products  of  change  exert  no  specific 
influence  in  this  case :  indeed,  the  addition  of  the 
equivalent  quantity  of  a  neutral  salt  brings  about  a 
similar  acceleration. 

The  fermentation  of  glucose  by  yeast  juice  supplies 
another  instance  of  the  more  complicated  character  of 
enzyme  actions  as  compared  with  changes  which  are 
accelerated  by  inorganic  catalysts.  It  has  been  found 
that  the  ferment  in  yeast  juice  is  of  itself  unable  to 
bring  about  the  alcoholic  fermentation  of  glucose ;  another 
body,  the  'co-ferment,'  as  it  is  called,  which  is  present 
in  yeast  juice,  is  essential  to  the  activity  of  the  ferment.2 
A  separation  of  the  ferment  and  co-ferment  is  effected 

1  See  Armstrong,  Proc.  Roy.  Soc.,  1904,  73,  520. 

2  See  Harden  and  Young,  Proc.  Roy.  Soc.,  B,  1906,  77,  405  ;  78,  369. 


300  PHYSICAL  CHEMISTKY 

by  dialysis;  the  residue,  containing  the  ferment,  and 
the  dialysate,  containing  the  co-ferment,  are  separately 
inactive,  but  when  united  give  rise  to  fermentation. 
The  inactive  residue  obtained  on  dialysis  can  be  rendered 
active  also  by  the  addition  of  boiled  and  filtered  yeast 
juice;  it  follows,  therefore,  that  the  co-ferment  is  not 
destroyed  by  boiling.  During  the  process  of  fermen- 
tation the  co-ferment  disappears,  as  has  been  shown 
by  experiments  in  which  a  fairly  large  quantity  of  the 
inactive  residue  from  dialysis  and  a  small  quantity  of 
boiled  yeast  juice  have  been  added  to  a  glucose  solution. 
In  this  case  the  evolution  of  carbon  dioxide  soon  comes 
to  an  end,  but  on  the  addition  of  a  further  quantity 
of  boiled  juice  fermentation  is  set  up  again. 

The  Mechanism  of  Catalysis. — The  phenomena  of 
catalysis  generally,  and  more  particularly  those  of  enzyme 
action,  give  rise  to  the  question  :  How  does  the  catalyst 
exert  its  influence  ?  In  the  present  state  of  our  know- 
ledge it  is  impossible  to  give  a  complete  and  satisfactory 
answer  to  this  question,  but  it  is  desirable  to  indicate 
some  of  the  main  facts  which  have  a  bearing  on  the 
problem,  and  some  of  the  suggestions  which  have  been 
contributed  towards  its  solution. 

It  will  be  convenient  to  start  from  the  suggestion, 
which  has  been  very  generally  accepted,  that  a  catalyst 
is  effective  because  it  forms  some  sort  of  combination 
with  the  substrate.  This  intermediate  compound,  it  is 
supposed,  then  breaks  up  into  the  final  products  of 
change,  the  catalyst  being  liberated.  Obviously,  if  this 
account  of  the  catalytic  change  is  to  give  an  adequate 
interpretation  of  the  phenomena,  it  is  necessary  to  sup- 
pose that  the  formation  and  decomposition  of  the  inter- 
mediate compound  together  require  a  much  shorter  time 
for  their  occurrence  than  the  direct  change  itself. 


VELOCITY   OF  CHEMICAL  EEACTION     301 

In  favour  of  the  view  that  combination  of  some  kind 
takes  place  between  catalyst  and  substrate  there  is  a 
considerable  amount  of  evidence.  As  found  by  0 'Sullivan 
and  Tompson,1  invertase  in  the  presence  of  sucrose  stands 
without  injury  exposure  to  a  temperature  25°  higher 
than  it  does  in  the  absence  of  sucrose.  Similarly,  pro- 
teins exert  a  protective  influence  over  trypsin.2  More 
direct  evidence  of  the  formation  of  intermediate  com- 
pounds has  been  brought  forward  by  Erode  3  in  his  study 
of  the  accelerating  influence  of  molybdic  acid  on  the 
reaction  between  hydrogen  peroxide  and  hydrogen  iodide. 
In  this  case  it  can  be  proved  that  combination  takes 
place  between  the  molybdic  acid  and  the  hydrogen 
peroxide,  with  the  result  that  the  former  is  practically 
converted  into  permolybdic  acid.  It  is  then  supposed 
that  the  reduction  of  this  substance  by  hydriodic  acid 
takes  place  much  more  rapidly  than  the  reduction  of 
hydrogen  peroxide.  Other  facts  in  favour  of  the  view 
that  catalysts  act  by  forming  intermediate  compounds 
are  the  occurrence  of  a  linear  portion  in  the  time  curve 
for  the  hydrolysis  of  sugars  by  relatively  small  quantities 
of  the  appropriate  enzymes  (see  p.  295),  and  also  the 
specificity  of  enzymes.  But  although  we  may  with  some 
confidence  assume  the  formation  of  intermediate  com- 
pounds in  enzyme  action  and  catalysis  generally,  it  is 
quite  impossible  in  the  majority  of  cases  to  specify  the 
nature  of  these  compounds. 

In  this  connection  it  must  be  borne  in  mind  that 
many  catalytic  reactions  are  to  be  described  as  non- 
homogeneous  reactions,  as,  for  instance,  the  union  of 
hydrogen  and  oxygen  under  the  influence  of  platinum 
black.  Here  the  catalyst  is  solid,  whilst  the  reacting 

1  Journ.  Chem.  Soc.,  1890,  57,  834. 

2  Bayliss  and  Starling,  Journ.  PhysioL,  1904,  30,  61. 

j>  Zeit.  physikal.  Chem.,  1901,  37,  257.     See  also  p.  286. 


302  PHYSICAL   CHEMISTRY 

substances  are  both  gaseous';  the  system  is  a  '  two-phase  ' 
one.  Solutions  of  colloidal  platinum  and  solutions  of 
enzymes,  which  are  colloids,  are  also  to  be  regarded  as 
two-phase  systems,  and  in  such  cases  there  is  the  possi- 
bility of  a  surface  concentration  and  the  formation  of 
adsorption  compounds,  such  as  those  described  in  Chapter 
XI.  The  combination  between  catalyst  and  substrate, 
according  to  this  view,  would  be  more  physical  than 
chemical  in  type. 

In  connection  with  the  velocity  of  reaction  in  non- 
homogeneous  systems,  doubt  has  been  expressed  whether 
in  all  such  cases  one  is  actually  measuring  the  rate  of 
a  chemical  change.  Nernst 1  has  pointed  out  that  a 
reaction  in  a  non-homogeneous  system  involves,  in  ad- 
dition to  a  chemical  change,  a  diffusion  of  various  sub- 
stances to  and  from  the  common  boundary  of  the  two 
phases.  It  is  therefore  evident  that  where  the  rate 
of  the  chemical  change  is  relatively  very  great,  the 
observed  velocity  of  reaction  may  be  merely  a  diffusion 
velocity.  An  actual  example  of  this  is  found  in  the 
rate  of  solution  of  marble  and  various  metals  in  acids, 
and  Nernst  has  suggested  that  the  velocity  of  decomposi- 
tion of  hydrogen  peroxide  by  colloidal  platinum  is  deter- 
mined by  the  rate  of  diffusion  of  the  peroxide  to  the 
surface  of  the  platinum  particles.  While  this  may  be  so, 
the  theory  cannot  be  regarded  as  applicable  to  all  reac- 
tions in  non-homogeneous  systems. 

The  Temperature  Coefficient  of  Reaction  Velocity.— 

It  is  well  known  that  the  velocity  of  a  chemical  reaction 
increases  very  rapidly  as  the  temperature  rises,  and 
as  a  result  of  this  the  range  of  temperature  over  which 
quantitative  investigation  of  the  velocity  of  a  reaction 
is  possible  is  comparatively  limited.  So  far  as  reactions 

1  Zeit.  phy sikal.  Chem.,  1903,  47,  52;  also  Brunner,  ibid.,  56. 


VELOCITY  OF   CHEMICAL   REACTION     303 

in  "homogeneous  systems  are  concerned,  it  is  found  that, 
as  a  general  rule,  the  velocity  is  doubled  or  trebled  for 
a  rise  of  10°  .C.  Reactions  of  the  most  varied  character 
conform  to  this  rule,  but  the  inversion  of  sucrose  by 
acid  will  serve  as  an  example.  The  accompanying  table 
gives  the  values  of  k,  the  velocity  coefficient  for  this 
reaction,  at  temperatures  between  25°  and  55°.  These 

Temperature.  *. 

25°  9-67 

40°  73-4 

45°  139 

50°  268 

55°  491 

figures  are  a  quantitative  expression  of  the  increase 
of  velocity  with  rise  of  temperature,  and  it  will  be 

seen  that  in  this  case  -^-°  lies  between  3  and  4.     The 

JcT 

average,  however,  of  the  temperature  coefficient  for  a 
reaction  in  a  homogeneous  system  is  between  2  and  3. 

The  value  of  the  temperature  coefficient  for  a  non- 
homogeneous  reaction  is  frequently  found  to  be  con- 
siderably lower.  The  influence  of  temperature  on  the 
catalysis  of  hydrogen  peroxide  by  colloidal  platinum1 

may  be  quoted  as  an  instance;    in  this  case  ^±i?  =  i«7 

KT 

while  for  the  catalysis  of  hydrogen  peroxide  by  hsemase 

^±1°  =  1'5.      These   values   are    not   much   greater   than 

kT 

the  value  (about  1'3)  we  should  expect  if  the  rate  of 
reaction  were  determined  by  a  diffusion  velocity  alone, 
and  it  is  therefore  probable  that  in  finding  the  velocity 
of  catalysis  in  both  these  cases  one  is  measuring  the 
velocity  of  a  physical  process,  not  of  a  chemical  change. 


1  JJredig  and  von  Berneclc,  Zeit.  physikal.  Chem.,  1899,  31,  258. 

V 


304  PHYSICAL   CHEMISTRY 

In  the  case  of  most  enzyme  actions,  however,  the  tem- 
perature coefficient  is  considerably  higher  than  that 
corresponding  to  a  diffusion  velocity,  and  is  of  the 
same  order  as  that  usually  observed  for  chemical  reactions 
in  homogeneous  systems.1 

The  relation  between  temperature  and  enzyme  action 
is  complicated  to  some  extent  by  the  occurrence  of  a 
so-called  '  optimum '  temperature.  An  example  of  this 
is  found  in  the  hydrolysis  of  salicin  by  emulsin.2  The 
velocity  of  this  hydrolysis  at  various  temperatures  is 
represented  in  the  accompanying  table,  the  velocity  at 

t°  C.  Velocity. 

0  1-0 

20-5  2-3 

30-0  5'8 

40-2  8-8 

50-3  15-8 

60-6  13'3 

70-0  12-3 

0°  being  taken  as  unity.  In  the  neighbourhood  of  50° 
there  is  a  point,  the  optimum  temperature,  at  which 
hydrolysis  proceeds  more  rapidly  than  at  any  other 
temperature.  The  existence  of  such  a  point  must  not 
be  taken  to  indicate  the  abrogation  of  the  rule  that 
reaction  velocity  increases  rapidly  with  rise  of  tem- 
perature. The  falling  off  in  the  velocity  at  the  higher 
temperatures  is  due  to  the  destruction  of  the  enzyme, 
and  the  diminution  in  the  effective  quantity  of  the 
catalyst  more  than  counterbalances  the  increase  in 
the  velocity  which  rise  of  temperature  invariably 
brings  about.  All  colloidal  systems  are  liable  to  be 
affected  in  a  similar  way  by  rise  of  temperature,  and 

1  See  Senter,  Journ.  Physical  Qhem.,  1905,  9,  311. 

2  Tammann,  Zeit.  physiol.  Chem.,  1892,  16,  323. 


VELOCITY  OF  CHEMICAL  EEACTION     305 

it  is  therefore  not  surprising  that  .there  is  an  optimum 
temperature  for  the  union  of  hydrogen  and  oxygen 
under  the  influence  of  colloidal  platinum  solution. 
In  an  experiment  described  by  Ernst,1  2  cub.  cm. 
of  a  solution  of  colloidal  platinum  were  shaken  at  25° 
with  electrolytic  gas,  and  the  decrease  in  volume  in 
3  minutes  was  1*02  cub.  cm.  When  2  cub.  cm.  of 
the  same  platinum  solution  were  kept  at  45°  for  two 
hours  and  then  shaken  with  electrolytic  gas  at  this 
temperature,  the  decrease  in  volume  in  3  minutes  was 
1*41  cub.  cm.  The  corresponding  figures  for  65°  and 
85°  were  1*46  and  1*26,  showing  the  existence  of  an 
optimum  temperature. 

It  is  a  striking  fact  that  the  acceleration  of  various 
vital  processes  produced  by  rise  of  temperature  is  very 
similar  to  that  observed  for  ordinary  chemical  reactions. 
This  is  the  case,  for  instance,  with  vegetable  .respiration.2 
Investigation  of  cherry-laurel  leaves  has  shown  that 
at  45°  the  output  of  carbon  dioxide  per  unit  weight 
of  leaf  is  0-0210  gram  per  hour,  whereas  at  16 '2°  the 
amount  is  only  0'0025  gram  per  hour.  According  to 
these  figures,  the  temperature  coefficient  for  a  rise  of 
10°  is  2'1,  in  good  agreement  with  the  value  found 
for  the  temperature  coefficient  of  chemical  reactions 
generally.  In  regard  also  to  assimilation  of  carbon 
dioxide  at  medium  temperatures,  the  same  relation  exists 
between  reaction  velocity  and  temperature.  Other  cases 
where  the  temperature  coefficient  of  velocity  has  been 
determined  for  changes  in  which  living  matter  is  in- 
volved are  the  development  of  sea-urchin  and  fish  eggs,3 
the  action  of  drugs  on  muscle,4  and  the  conduction  of 

1  Zeit.  physikal.  Chem.,  1901,  37,  475. 

2  Matthaei,  Phil.  Trans.,  B,  1905,  197,  47. 

3  Abegg,  Zeit.  Elektrochem.,  1905,  11,  528  ;  Herzog,  ibid.,  820. 

4  Veley  and  Waller,  Proc.  Roy.  Soc.,  B,  1910,  82,  205. 


306  PHYSICAL  CHEMISTRY 

an   impulse  along   a  nerve.1     The  value  found  for  -|±!0 

KT 

varies  somewhat  from  case  to  case,  but  is  in  all  in- 
stances of  the  same  order  as  that  found  for  chemical 
reactions. 

1  Lucas,  Journ.  Physiol  ,  1908,  37, 112, 


CHAPTER   XIV 

ELECTROMOTIVE   FORCE 

REFERENCE  has  been  made  in  an  earlier  chapter 
(pp.  158-9)  to  the  circumstances  in  which  a  potential 
difference  may  originate  at  the  common  surface  of  two  salt 
solutions  or  at  the  surface  of  a  membrane  bathed  by  an 
electrolyte.  Such  potential  differences,  although  of  im- 
portance in  the  interpretation  of  electro-physiological 
phenomena,  are  usually  of  a  small  order  of  magnitude. 
They  are  much  smaller,  as  is  well  known,  than  the 
differences  of  electric  potential  which  exist  at  the  surface 
of  a  metal  immersed  in  a  salt  solution.  Now,  although 
the  conjunction  of  metal  and  salt  solution  does  not  occur 
with  physiological  fluids  in  their  natural  condition,  it  is 
found  that  valuable  information  regarding  the  nature  of 
these  fluids  may  sometimes  be  obtained  by  bringing  them 
in  contact  with  an  electrode  and  measuring  the  potential 
difference  which  is  developed.  In  order  to  understand 
this  method  of  investigating  physiological  fluids,  it  will 
be  necessary  to  consider  a  little  in  detail  what  are  the 
•conditions  of  equilibrium  between  an  electrode  and  the 
solution  in  which  it  is  immersed,  and  what  are  the 
factors  which  determine  the  potential  difference. 

Electrolytic  Solution  Tension  and  Potential  Differ- 
ence.— It  is  customary  to  regard  a  metal  as  possessing  a 
certain  tendency  to  give  off  positively  charged  ions  when 
it  is  immersed  in  water  or  in  an  aqueous  solution.  The 

307 


308  PHYSICAL  CHEMISTRY 

magnitude  of  this  tendency,  the  electrolytic  solution  ten- 
sion, as  it  is  called,  varies  from  one  metal  to  another  :  it 
is  high,  for  instance,  in  the  case  of  zinc ;  it  is  low  for 
copper.  So  great  is  the  difference  in  the  electromotive 
behaviour  of  these  two  metals,  that  whereas  a  rod  of  zinc, 
immersed  in  a  solution  of  zinc  sulphate,  gives  off  positive 
metallic  ions  to  the  solution  and  is  itself  left  negatively 
charged,  a  rod  of  copper,  immersed  in  a  solution  of 
copper  sulphate,  assumes  a  positive  charge,  owing  to  the 
deposition  on  it  of  positive  ions  from  the  salt  solution. 
In  this  latter  case,  the  feeble  electrolytic  solution  tension 
of  the  copper  is  overcome  by  the  osmotic  pressure  of  the 
corresponding  metallic  ions  in  the  salt  solution,  and  some 
of  these  latter  are  deposited  on  the  metal.  It  will  be 
plain,  however,  that  in  any  case  the  discharge  of  metallic 
ions  into  the  solution,  or  the  deposition  of  ions  from  the 
solution  on  the  metal,  can  take  place  only  to  a  very 
limited  extent,  owing  to  the  electrostatic  forces  which 
come  into  play  between  the  separated  positive  and  nega- 
tive electricity. 

From  the  point  of  view  just  described  it  will  be  seen 
that  the  potential  difference  between  metal  and  solution 
depends  on  and  is  determined  by  the  relative  value  of 
the  electrolytic  solution  tension  of  the  metal  on  the  one 
hand  and  the  osmotic  pressure  of  the  metallic  ions  in  the 
solution  on  the  other  hand.  The  exact  relationship 
between  the  potential  difference  E,  the  solution  tension 
P  of  the  metal,  and  the  osmotic  pressure  p  of  the  metallic 
ions  in  the  solution  is  established  by  thermodynamics, 
but  the  proof  cannot  be  given  here:  it  must  suffice  to 
state  the  formula  and  explain  its  significance.  If  T  is 
absolute  temperature  and  n  is  the  valency  of  the  metal 

T>J1  P 

under  consideration,  then  .£f=96540^.  loge-,  R  being  the 
gas  constant  (see  p.  10).  By  making  a  change  to  ordi- 


ELECTROMOTIVE  FORCE  309 

nary  logarithms,  expressing  E  as  volt -coulombs  (i.e. 
^=•082x101-8,  since  1  litre-atmosphere  =101 -8  volt- 
coulombs),  and  taking  ^=290°,  corresponding  to  an 
average  room  temperature  of  17°  C.,  we  have  the  simpli- 
fied expression  E—  — :—  .  Iog10  -.  This  is  a  fundamental 

formula  expressing  the  potential  difference  (in  volts)  at 
the  junction  metal  |  salt  solution,  in  terms  of  the  valency 
of  the  metal,  the  osmotic  pressure  of  the  metallic  ions  in 
the  solution,  and  the  electrolytic  solution  pressure  of  the 
metal. 

From  the  standpoint  of  the  biologist  or  physiologist, 
the  most  significant  feature  of  the  foregoing  formula  is 
the  presence  in  it  of  the  quantity  p,  the  osmotic  pressure 
of  the  metallic  ions  in  the  solution  which  bathes  the 
metal  electrode.  For  it  follows  that  the  concentration 
of  the  ions  in  the  solution  is  a  factor  in  determining  the 
potential  difference,  and  a  little  consideration  of  the 
formula  enables  one  to  draw  the  quantitative  conclusion 
that  for  every  tenfold  increase  or  decrease  in  the  osmotic 
pressure  of  the  metallic  ions  there  is  a  change  in  the 
potential  difference  amounting  to  '058  volt  for  a 

univalent  metal,  and  —^-  volt  for  a  divalent  metal. 

A  first  illustration  of  the  part  played  by  the  osmotic 
pressure  of  the  metallic  ions  in  determining  the  potential 
difference  at  a  metal  electrode  may  be  taken  from  the 
well-known  Daniell  cell.  This  consists  of  a  zinc  rod 
immersed  in  a  solution  of  zinc  sulphate,  separated  by 
a  porous  pot  from  a  solution  of  copper  sulphate  in  which 
a  copper  electrode  dips ;  when  the  zinc  and  copper  poles 
are  connected  externally  with  a  metal  wire,  a  current 
flows  through  the  wire  from  the  copper  to  the  zinc.  In 
the  Daniell  cell,  represented  conveniently  as  Zn  |  ZnS04, 
CuS04  |  Cu,  there  are,  as  in  all  ordinary  galvanic  cells, 


310  PHYSICAL  CHEMISTRY 

two  places  where  the  junction  metal  |  solution  occurs, 
and  the  potential  difference  at  each  of  the  two  electrodes 
can  be  expressed  by  the  above  formula.  Neglecting  the 
slight  potential  difference  which  arises  at  the  common 
surface  of  the  two  solutions,  we  can  express  the  E.M.F. 
of  the  Daniell  cell  as  E^  —  Ev  where  E^  and  E2  are  the 
potential  differences  at  the  zinc  and  copper  electrodes 
respectively.  Now,  if  Pl  and  P2  are  the  electrolytic  solu- 
tion tensions  of  zinc  and  copper,  while  pl  and  pz  are  the 
osmotic  pressures  of  zinc  and  copper  ions  respectively  in 


the  two  solutions,  then  E^EZ=        loglo      -         loglog 

=  ~log10^-2,  and  the  E.M.F.   of  the  Daniell  cell  is 

accordingly  given  by  this  expression.  It  is  easy  to 
extract  from  this  formula  the  conclusion  that  by  diminish- 
ing pl  or  increasing  p2,  i.e.  by  diluting  the  zinc  sulphate 
solution  or  concentrating  the  copper  sulphate  solution, 
the  E.M.F.  of  the  Daniell  cell  should  be  raised.  Experi- 
ment shows  that  this  is  actually  the  case,  and  so  far,  at 
least,  the  osmotic  theory  of  galvanic  cells  is  confirmed. 

Concentration  Cells.  —  From  the  standpoint  adopted 
in  this  volume,  one  of  the  most  interesting  types  of  gal- 
vanic cell  is  the  so-called  "  concentration  cell,"  and  the 
application  of  the  osmotic  theory  to  this  case  is  of  great 
importance.  A  concentration  cell  is  to  be  conceived  as 
one  in  which  the  two  electrodes  are  of  the  same  metal, 
and  each  electrode  is  bathed  by  a  solution  containing  the 
corresponding  metallic  ions,  the  ion  concentrations  round 
the  two  electrodes,  however,  having  different  values.  In 
such  a  cell  there  are  three  places  at  which  differences  of 
potential  originate:  (1)  at  the  junction  metal  |  dilute 
solution  ;  (2)  at  the  junction  metal  |  concentrated  solu- 
tion ;  (3)  at  the  common  surface  of  the  two  solutions. 
In  the  case  of  concentration  cells,  the  E.M.F.  of  which  is 


ELECTROMOTIVE  FORCE  311 

generally  small,  the  potential  difference  between  the  two 
solutions  cannot  so  lightly  be  neglected  as  in  the  case  of 
the  Daniell  cell  above.  Whilst  the  potential  difference 
between  the  two  solutions  can  be  evaluated,  as  shown  by 
Nernst  and  Planck,  it  is  customary  in  practical  deter- 
minations l  of  the  E.M.F.  of  concentration  cells  to  elimi- 
nate it  altogether  by  interposing  between  the  two 
electrode  solutions  a  concentrated  solution  of  potassium 
chloride  or  potassium  nitrate.  For  reasons  which  cannot 
be  discussed  here,  this  procedure  practically  gets  rid  of 
the  potential  difference  between  the  two  electrode  solu- 
tions, so  that  the  measured  E.M.F.  of  the  cell  may  then 
be  taken  as  compounded  of  the  two  electrode  potentials. 
In  what  follows  it  will  be  assumed  that  the  liquid  poten- 
tial has  been  eliminated  in  the  way  described,  and  may 
therefore  be  neglected. 

Suppose  now  that  we  have  a  concentration  cell  with 
two  silver  electrodes  dipping  in  two  solutions  of  silver 
nitrate,  the  osmotic  pressure  of  the  silver  ions  in  the 
stronger  solution  being  pv  in  the  weaker  solution  p2. 
A  little  consideration  will  show  that  when  the  silver 
electrodes  are  connected  externally  by  a  wire,  current 
must  flow  in  the  cell  from  the  weaker  solution  to  the 
stronger,  for  the  working  of  the  cell  must  tend  to 
diminish  the  difference  in  the  concentrations  of  the 
electrode  solutions.  If  E  represents  the  electromotive 
force  of  this  silver  nitrate  concentration  cell,  then  E 

=  '058  loglo  £-'058  Iog10  £='058  loglo^;   as  the  two 

electrodes  are  of  the  same  metal,  the  electrolytic  solution 
tension  disappears  from  the  formula.  The  electromotive 
force  of  such  a  cell  is  thus  seen  to  be  determined  simply 

1  For  a  description  of  the  usual  compensation  method  of  determin- 
ing the  E.M.F.  of  galvanic  cells,  a  text-book  of  practical  physical 
chemistry  should  be  consulted. 


312  PHYSICAL  CHEMISTRY 

by  the  ratio  of  the  osmotic  pressures  of  the  ions  in  the 
electrode  solutions  ;  and  if  it  is  borne  in  mind  that  osmotic 
pressure  is  proportional  to  concentration,  we  may  write 

j£='058  Iog10  -,  where  cx  and  c2  are  the  ion  concentra- 
tions in  the  stronger  and  weaker  solutions  respectively. 

With  the  help  of  the  formula  just  developed,  it  is  easy 
to  calculate  the  electromotive  force  of  a  silver  nitrate 
concentration  cell,  such,  for  instance,  as  the  one  repre- 
sented by  Ag  |  ^AgN03,  ^AgNOg  Ag.  The  concen- 
trations of  the  silver  nitrate  in  the  two  electrode  solutions 
are  O'l  and  O'Ol  respectively,  but  in  order  to  get  the 
values  of  cx  and  c2,  the  concentrations  of  the  silver  ion, 
a  knowledge  of  the  degrees  of  electrolytic  dissociation  in 

N  N 

^AgN03  and  ^AgNOg  is  necessary.    From  conductivity 

measurements  these  are  found  to  be  0*82  and  0'94  re- 
spectively, so  that  ^=0-1  x  0-82,  and  c2=  O'Ol  X  0-94. 

'082 

Hence  JZ=  *058  x  Iog10  ^^=-055  volt,  a  value  which  is 

in  good  agreement  with  the  experimentally  determined 
figure. 

Just  as  for  silver  concentration  cells,  so  also  for  the 

case  of  other  univalent  metals,  J^  =  *058  Iog10  -1.     It  is 

easily  seen  that  if  the  electromotive  force  of  a  concen- 
tration cell  of  this  type  has  been  determined,  and  if  the 
ion  concentration  round  one  electrode  is  known,  the  ion 
concentration  round  the  other  electrode  can  be  calculated. 
This  principle  has  found  useful  application  in  the  de- 
termination of  very  small  ion  concentrations,  and  has 
been  employed,  for  instance,  in  finding  the  solubility  of 
sparingly  soluble  salts.  As  an  illustration  of  the  ap- 
plication of  the  principle,  the  problem  of  finding  the 
solubility  of  silver  iodide  may  ^)e  taken.  For  this 


ELECTROMOTIVE   FORCE  313 

purpose  a  concentration  cell  represented  by  the  scheme 

+       1000  _j_       }    Ag  is  set  up,  the  potassium  nitrate 
KNO3         KN03 
being  added  in  order  to  diminish  the  resistance  of  the 
cell,  and  to  eliminate  the  liquid  potential,  as  already  de- 
scribed.    The  solution  round  one  electrode  is 


and,  as  this  is  very  dilute,  the  silver  ion  concentration 


FIG.  24. 

in  this  solution  may  be  taken  as  '001,  the  electrolytic 
dissociation  being  practically  complete.  The  other  elec- 
trode is  bathed  by  a  saturated  solution  of  silver  iodide — 
a  solution  in  which  plainly  the  silver  ion  concentration 
is  exceedingly  small.  Experiment  shows  that  the  E.M.F. 
of  the  concentration  cell  just  described  is  0'22  volt,  so 

'001 

that  we  have  0'22  —  '058  Iog10  ,  where  c2  is  the  con- 
centration of  the  silver  ions  in  the  saturated  solution  of 
silver  iodide.  This  equation  gives  c2=l'6  x  10  ~8  equiva- 
lents per  litre,  and  since  the  dissociation  of  the  silver 


314  PHYSICAL  CHEMISTRY 

iodide  may  be  taken  as  complete  at  such  a  great  dilution, 
the  figure  l'6x!0~8  represents  also  the  concentration  of 
silver  iodide  in  its  saturated  solution,  and  that  is  simply 
the  solubility  of  the  salt. 

In  setting  up  concentration  cells  and  in  the  deter- 
mination of  electrode  potentials  generally,  it  is  con- 
venient to  use  separate  electrode  vessels,  which  can  each 
be  charged  with  their  own  particular  solutions  and  then 
connected  by  means  of  an  intermediate  vessel.  The 
foregoing  Fig.  24  shows  two  electrode  vessels  which  are 
in  liquid  connection  with  the  contents  of  an  intermediate 
beaker ;  the  latter  contains  a  strong  solution  of  potas- 
sium nitrate  or  potassium  chloride,  in  order  to  eliminate 
the  potential  difference  between  the  electrode  solutions, 
as  already  described. 

The  Hydrogen  Electrode  and  its  Applications. — In 

the  foregoing  discussion  of  concentration  cells,  it  has 
been  implied  that  the  electrodes  are  invariably  of  metal 
and  are  the  scene  of  a  reversible  equilibrium  between  a 
metal  and  its  ions  in  the  surrounding  solution.  This 
conception,  however,  must  be  extended  to  cover  cases 
where  the  electrode  substance  is  really  a  gas,  this  being 
in  contact  with  a  solution  containing  the  same  substance 
in  the  ionised  condition.  Since  hydrogen  is  the  gas 
which  has  chief  significance  in  this  connection,  it  is  de- 
sirable to  refer  to  it  more  especially,  and,  first  of  all,  to 
describe  the  hydrogen  electrode. 

The  vessel  which  is  to  serve  in  the  construction  of  a> 
hydrogen  electrode  is  similar  to  one  of  those  depicted  in 
Fig.  24,  but  must  be  modified  so  as  to  permit  a  current- 
of  hydrogen  gas  to  be  bubbled  through  the  solution :  the 
modification  consists  in  sealing  on  a  narrow  tube  at  the 
bottom  of  the  electrode  vessel.  The  electrode  itself  is  a 
piece  of  platinum  foil  coated  with  platinum  black  (see 


ELECTROMOTIVE   FORCE  315 

p.  125),  or  a  thin  film  of  platinum  on  glass,  in  either  case 
saturated  with  hydrogen  gas  and  half  immersed  in  an 
acid  solution,  i.e.  a  solution  containing  hydrogen  ions. 
When  sufficient  time  has  been  allowed  for  the  solution 
and  the  platinum  to  become  completely  saturated  with 
the  gas,  this  "  hydrogen  electrode "  has  a  perfectly 
definite  and  steady  potential,  the  numerical  value  of 
which  is  defined  by  the  pressure  of  the  hydrogen  gas 
and  the  osmotic  pressure  of  the  hydrogen  ions  in  the 
surrounding  solution. 

In  like  manner  one  may  construct  a  chlorine  electrode 
or  an  oxygen  electrode.  In  the  latter  case  the  platinum 
foil  or  film,  saturated  with  oxygen,  is  immersed  in  an 
alkali  solution,  which  may  be  regarded  as  containing 
oxygen  ions,  derived  from  the  hydroxyl  ions  which  are 
mainly  present,  thus:  20H'  J0"4-H20. 

Reverting  to  the  hydrogen  electrode,  it  is  easily  seen 
that,  on  the  basis  of  the  parallelism  between  this  electrode 
and  the  metal  electrodes  already  described,  concentration 
cells  may  be  constructed,  the  E.M.F.  of  which  will  be 
determined  solely  by  the  relative  concentration  of  the 
hydrogen  ion  round  the  two  electrodes.  That  is,  if  cx 
and  c2  are  the  concentrations  of  the  hydrogen  ion  in  the 
stronger  and  weaker  acid  solutions  at  the  electrodes  of 
a  hydrogen  concentration  cell,  the  electromotive  force  of 

the  cell  at  17°  C.  is  given  by  the  formula  E=  -058  Iog10  ^, 

supposing  that  the  potential  at  the  common  surface  of 
the  two  solutions  has  been  eliminated.  This  formula 
not  only  allows  the  calculation  of  the  electromotive  force 
of  a  hydrogen  concentration  cell  from  the  concentrations 
of  the  hydrogen  ion  in  the  two  electrode  solutions — a 
calculation  that  is  verified  experimentally — but  permits 
the  evaluation  of  the  hydrogen  ion  concentration  in  the 
one  electrode  solution,  provided  the  electromotive  force 


316  PHYSICAL  CHEMISTRY 

of  the  cell  and  the  hydrogen  ion  concentration  in  the 
other  electrode  solution  are  known.  In  order,  therefore, 
to  find  the  hydrogen  ion  concentration  in  any  given 
liquid,  the  latter  is  made  one  of  the  electrode  solutions 
in  a  hydrogen  concentration  cell,  while  dilute  hydro- 
chloric acid  of  known  strength  is  taken  for  the  other 
electrode  solution.  This  method  is  particularly  suited 
for  determining  very  small  hydrogen  ion  concentrations, 
for,  the  greater  the  difference  between  c±  and  c2,  the 
higher  is  the  electromotive  force  of  the  concentration 
cell. 

As  a  first  example  of  the  application  of  this  method 
of  finding  the  hydrogen  ion  concentration  in  aqueous 
solutions,  we  may  take  the  problem  of  determining  the 
ionisation  of  water.1  It  has  been  already  explained 
(p.  259)  that  the  application  of  the  law  of  mass  action 
to  the  equilibrium  between  water  and  its  ions  leads  to 
the  result  that  if  CH  and  COH  represent  the  concentra- 
tions of  the  hydrogen  and  the  hydroxyl  ions  respectively 
in  any  aqueous  solution,  then  CH.COH= const.  Now,  one 
method  of  getting  the  value  of  this  "ionic  product"  for 
water  depends  on  the  measurement  of  the  E.M.F.  of  the 
hydrogen  concentration  cell  represented  by  the  scheme : 

N  N  N 

H2  jQ^HCl  YggNaCl  ^NaOH  H2.     In  this  arrangement 

H2  I  ™HC1  and  H2    -  _NaOH  represent  the   hydrogen 

electrodes,  the  two  electrode  solutions  being  connected 
through  an  intermediate  solution  of  sodium  chloride. 
The  latter  is  introduced  in  order  to  avoid  the  trouble- 
some calculation  of  the  potential  difference  which  would 

N  N 

arise  if  the  ^HCl  and  r— NaOH  were  directly  in  contact. 


The  potentials  at  the  junctions  of  j^HCl  with  ^ 
1  gee  Lowenherz,  Zeit.  physical.  Chem.,  1896,  20,  284. 


ELECTROMOTIVE  FORCE  317 

and  of       NaCl  with       NaOH  on  the  other  hand,  can  be 


calculated  easily  with  the  help  of  the  Nernst-Planck 
formula,1  and  at  25°  are  respectively  '0307  volt  and  '0152 
volt.  In  the  hydrogen  concentration  cell  under  consider- 
ation, the  positive  current  flows  inside  the  cell  from  the 
alkali  solution  to  the  acid  solution,  and  the  total  E.M.F. 
of  the  cell,  determined  by  actual  measurement,  is  0*5378 
volt  at  25°.  The  two  liquid  potentials  referred  to  are 
both  opposed  in  direction  to  the  electrode  potentials,  so 
that  if  E  represents  the  E.M.F.  compounded  of  the 
electrode  potentials  alone,  J£=0-5378  +  O0307+  0-0152 

=  0-5837  volt.  But  at  25°  2  J£=-059  Iog10  ^,  where  ^  is 
the  concentration  of  hydrogen  ion  in  ^HCl,  and  c2  is 

the  concentration  of  hydrogen   ion  in  j^NaOH  ;    and 

since  conductivity  measurements  show  that  hydrochloric 

N 
acid  in  ^  solution  is  electrolytically  dissociated  to  the 

extent  of  97'6  per  cent.,  ^=0-01  X  0-976  =  '00976.  Hence 
we  have  0-5837-  -059  Iog10  -°^,  from  which  it  follows 
that  cz=  1-257  X  10~12.  The  degree  of  dissociation  of 
sodium  hydroxide  in  ^  solution  is  0'935,  so  that  the 

concentration  of  the  hydroxyl  ions  in  r^~NaOH  is  "00935. 
Values  have  now  been  obtained  for  the  concentrations 
of  both  hydrogen  and  hydroxyl  ions  in  y^NaOH,  and 

the  ionic  product  for  this  solution=CH.COH=l'257  X  10~12 
X  -00935  =  1-2  xlO~14.  According  to  the  law  of  mass 

1  Ann.  Physik,  1890,  40,  561. 

2  The  higher  temperature  involves  an  increase  in  the  coefficient  of 
Iog10  ^,  the  value  '058  having  been  deduced  for  17°  C« 


318  PHYSICAL  CHEMISTRY 

action,  the  value  of  the  product  CH.COH  at  a  given  tem- 
perature is  the  same  in  water  as  in  any  aqueous  solution, 
and,  since  in  pure  water  CH=COH,  it  follows  that  the 
concentration  of  hydrogen  ion  in  pure  water  and  the  con- 
centration of  hydroxyl  ion  in  pure  water  are  each  given 
by  v/1-2  x  10-14,  that  is,  1-1  x  10  ~7. 

The  example  just  discussed  in  detail  shows  clearly  the 
utility  of  the  hydrogen  concentration  cell  in  the  deter- 
mination of  minute  concentrations  of  hydrogen  ion.  For 
this  purpose  the  electrometric  method  has  the  advantage 
over  other  methods  (see,  for  example,  pp.  167-8),  which 
are  adapted  rather  to  the  measurement  of  larger  concen- 
trations of  the  ion  in  question.  The  extent  of  hydrolytic 
dissociation  of  a  salt,  for  instance,  is  a  quantity  that  can 
readily  be  ascertained  by  the  electrometric  method. 
Suppose  it  were  desired  to  find  the  extent  of  hydrolysis  — 
in  other  words,  the  concentration  of  the  hydroxyl  ion  —  in 

^yr^r  sodium  acetate  solution.     This  can  be  done  by  set- 

1UUU  * 

ting  up  the  concentration  cell  represented  by  the  scheme  : 

H,  I  1555  HC1  I  m>  Na01  I  lM>CH3COONa  |  H2,  deter- 
mining  the  E.M.F.  of  this  cell,  and  then  calculating  the 
hydrogen  ion  concentration  in  the  CHgCOONa  as 


already  described.  When  the  hydrogen  ion  concentra- 
tion has  thus  been  ascertained,  that  of  the  hydroxyl  ion 
can  easily  be  calculated,  for,  as  shown  in  the  last  para- 
graph, the  product  of  the  two  concentrations,  CH  X  COH, 
has  a  constant  value,  which  at  25°  is  1/2  =  10~14. 

The  first  instance  of  the  application  of  the  foregoing 
electrometric  method  in  connection  with  more  definitely 
physiological  problems  is  furnished  by  Bugarszky  and 
Liebermann's  work  1  on  the  relation  between  protein  and 

1  Pfluger's  Arch.,  1898,  72,  5J. 


ELECTROMOTIVE   FORCE  319 

electrolytes.  The  acid-alkali  concentration  cell  described 
on  p.  316  was  employed  in  this  investigation,  and  the 
effect  of  adding  protein  either  to  the  acid  or  the  alkali 
was  studied  quantitatively.  In  this  way  definite  infor- 
mation was  obtained  as  to  the  influence  of  protein  on  the 
concentration  of  hydrogen  ion  in  a  given  acid  solution 
and  on  the  concentration  of  hydroxyl  ion  in  a  given 
alkali  solution.  The  results  showed  that  albumin  has 
the  power  of  combining  both  with  acid  and  with  alkali.1 

Concentration  of  Hydrogen  Ions  in  Physiological 
Fluids. — The  determination  of  the  exact  degree  of 
acidity  or  alkalinity  of  a  physiological  fluid  by  the 
ordinary  titrauon  methods  is  not  an  easy  matter.  In 
these  circumstances  the  measurement  of  the  hydrogen 
ion  concentration  by  the  electrometric  method  furnishes 
valuable  information.  Blood  has  frequently  been  ex- 
amined in  this  way,2  and  by  the  determination  of  the 

E.M.F.    of    such   concentration   cells    as   H2    y— .  HC1  + 

z  I  100 

f  NaCl  I  ?  NaCl  I  Blood  I  H2,  it  has  been  shown  that  the 

o  I    o  I  I 

concentration  of  hydrogen  ion  in  fresh  defibrinated  mam- 
malian blood  is  0*3  X  10~7  —  O7x  10~7  at  ordinary  tem- 
perature. Since  the  concentration  of  hydrogen  ion  in 
water  at  ordinary  temperature  is  0'8  X  10~7,  it  appears 
that  defibrinated  mammalian  blood  is  practically  a  neutral 
liquid.  It  is  worth  noting,  however,  that  if  in  the 
measurement  of  the  E.M.F.  of  the  gas  cell,  a  current 
of  hydrogen  is  passed  through  the  blood,  with  the  result 
that  the  carbon  dioxide  normally  present  in  this  fluid  is 
removed,  then  a  distinctly  lower  value,  viz.,  O'Ol  x  10~7  — 
0'03  X  10~7,  is  obtained  for  the  hydrogen  ion  concentra- 

1  See  p.  205,  and  cp.  Robertson,  J.  Physical  Ckem.,  1910, 14,  528. 

2  Hober,  Pfliiger's  Arch.,  1900,  81,  522  ;  1903,  99,  572  ;  Michaelis  and 
Eona,  Biochem.  Zeit.,  1909,  17,  317  ;  Hasselbalch,  ibid.,  1910,  30,  7. 

X 


320     p  PHYSICAL  CHEMISTRY 

tion.  This  figure  corresponds  with  a  feebly  alkaline  re- 
action. Rise  of  temperature  also  appears  to  favour 
alkalinity,  for  electrometric  measurements,  similar  to  the 
above  but  carried  out  at  37—38°,  indicate  that  at  body 
temperature  the  concentration  of  hydroxyl  ions  in  the 
blood  is  somewhat  greater  than  at  ordinary  temperature. 

The  examination  of  other  body  fluids  on  the  same  lines 
as  those  described  for  blood  has  confirmed  the  earlier 
conclusion  that  in  the  case  of  the  higher  animals  these 
fluids  are  generally  neutral.  Those  which  exhibit  a 
notable  departure  from  neutrality  are  gastric  juice,  pan- 
creatic juice,  intestinal  juice,  and  urine.  Hydrogen  cell 
measurements  have  shown  that  in  the  case  of  gastric 
juice  CH  (concentration  of  hydrogen  ion)  has  the  value 
3  x  10~2  —  9  X  10~2,  whilst  in  the  pancreatic  juice  and  the 
intestinal  juice  CH=7  X  1Q-10- 11  X  lO"10.  The  acidity 
of  the  urine,  even  for  a  single  individual,  varies  within 
wide  limits,  and  the  value  of  CH  may  be  put  down  as 
lxlO-7-lxlO-5. 

Reference  has  already  been  made  to  the  difficulty  of 
ascertaining  the  acidity  or  alkalinity  of  a  physiological 
fluid  by  the  ordinary  titration  methods.  These  methods 
involve  the  use  of  indicators,  and  it  is  a  well-known  fact, 
that  many  indicators  undergo  change  of  colour  before  the 
point  of  absolute  neutrality  (i.e.  CH  — COH)  is  reached. 
Thus,  for  instance,  the  turning  point  lies  at  CH=10~l!4  — 
10-2.e  for  tropaolin  00,  at  CH^lO-^-lO-4-4  for  methyl 
orange,  at  CH=10~5-°— 10~7'°  for  ^-nitrophenol,  and  at 
CH=10-8>3-10-10  for  phenolphthalein.1  Provided,  how- 
ever, that  the  turning  point,  in  terms  of  hydrogen  ion 
concentration,  is  known  for  each  of  a  large  number  of 
indicators,  then  with  the  help  of  such  a  "  set "  of  indi- 
cators the  degree  of  acidity  or  alkalinity  of  a  liquid  not 
far  from  the  point  of  neutrality  could  be  ascertained  with 

1  See  Sorensen,  Biochem.  Zeit.,  1909,  21,  131 ;  22,  352 ;  1910,  24,  381. 


ELECTROMOTIVE   FORCE  321 

fair  accuracy.  For  the  establishment  of  such  a  scale  of 
indicators  it  is  necessary  to  have  invariable  and  repro- 
ducible standards  of  acidity  and  alkalinity,  covering  more 
especially  the  range  from  CH=1  X  10~3  to  COH=1  x  10"3. 
For  this  purpose  the  solutions  obtained  by  mixing  sodium 
hydroxide  and  phosphoric  acid  in  different  proportions  are 
of  great  importance,1  the  exact  degree  of  acidity  or 
alkalinity  of  each  such  solution  being  determined  and 
controlled  electrometrically.  In  this  way  it  has  been 

found  that  for  ^NaH2P04  the  value  of  CH  is  1-2  X  10~4, 

while  for  ^Na2HP04  the  value  of  CH  is  l'4x  lO"9. 

With  a  suitable  "  set  "  of  indicators  available,  it  be- 
comes possible  to  ascertain  the  degree  of  acidity  or 
alkalinity  of  a  liquid,  and  Sorensen  (loc.  cit.)  has  investi- 
gated a  number  of  physiological  fluids  by  this  colori- 
metric  method.  The  method,  however,  must  be  used 
with  caution,  inasmuch  as  some  indicators  behave 
abnormally  in  presence  of  proteins  or  neutral  salts.  It 
is,  after  all,  on  physico-chemical  measurements  that  one 
depends  for  accurate  and  trustworthy  determinations  of 
the  concentration  of  the  hydrogen  ion  in  physiological 
fluids. 

1  See  Prideaux,  Biochem.  Journ.,  1911,  6,  122. 


SUBJECT  INDEX 


ABNORMAL  depression  of  freezing  point, 

115 

Absolute  temperature,  4 
Absorption  and  adsorption.  221 
Absorption  coefficient,  21,  22 
Absorption  of  gases,  20 

by  blood,  26 
Acid-alkali  cell.  316 
Accommodation  in  living  cells,  66,  67 
Acids,  strength  of,  252 
Additive  properties  of  salt  solutions,  139 
Adsorption,  219 

and  proteins.  238 

formula,  229 

theory  of  dyeing,  236 
Agglutination  and  adsorption,  240 

of  bacteria,  216 

of  blood  corpuscles,  218 
Air-bladder  of  fishes,  26 
Amphoteric  electrolytes,  261 
Antagonism  between  ions,  207 
Aquatic  plants,  gas  exchange  in,  24 
Artificial  parthenogenesis,  165 
Association  in  solution,  115 

BACTERIA,   accommodation  shown   by, 
64,  66 

agglutination  of,  216 
Barley  grains,  covering  of,  37 
Bimolecular  reactions,  283 
Blood,  alkalinity  of,  319 

conductivity  of,  136 

corpuscles  and  Lsotonic  solutions,  68 

corpuscles,  permeability  of,  161 

free7ing  point  of,  111 

gases  in,  26 

osmotic  strength  of,  70,  72 

serum,  osmotic  pressure  of,  181 
Boiling  point  and  molecular  weight,  35 

and  osmotic  pressure,  93 

of  solutions.  93 
Brownian  movement,  197 

CARBON  dioxide,  solubility  of,  21 

static  diffusion  of.  16 
Catalysis,  285 

mechanism  of,  300 
Catalysts,  inorganic.  286 
Catalytic  action  of  enzymes,  291,  294 
Cell  membranes,  nature  of,  82 

surface  tension  of,  855 


Coagulation  of  suspension  colloids,  201. 

208 
Colloidal  solutions  and  suspensions,  192 

filtration  of,  1C8 
Colloids.  177 

and  ions.  203.  211 

in  an  electric  field.  188 

in  biology.  214 
Colour  of  salt  solutions,  142 
Complete  reactions,  244 
Complex  ions,  173 
Concentration  cells,  310 
Concentration     changes     during     elec^ 

trolysis,  146 
Conductivity  and  fluidity,  156 

equivalent,  126 

ionic,  150 

measurement  of,  123 

of  physiologicaj  fluids.  136 

of  water,  170 

specific,  125 

Contractility  of  muscle,  102 
Copper,  toxic  action  of,  1 76 
Crystalloids.  177 

DA>OELL  cell.  309 
Degree  of  dissociation,  118,  130 
Density  and  molecular  weight,  9 
Dextrose  solutions,  osmotic  pressure  of, 

48,  51 

Dialysis,  178 
Diffusion  and  osmotic  pressure,  33 

as  factor  in  catalysis,  302 

of  colloids,  179 

of  electrolytes,  156 

of  gases.  13,  16 
Diffusion  of  gas  through  liquid  film,  22 

through  multiperforate  diaphragm, 

18 

Dilute  solutions.  44  '    ./ 
Dilution  law,  250 
Dissociation  constant,  251 

degree  of,  118,  130 

hydrolytic,  260 

in  solution,  117 

of  water,  170.  259,  316 
Distribution  ratio,  222 
Dyes,  adsorption  of,  235 

EFFUSION  of  gases,  15 
Electric  charge  on  protein.  191 


SUBJECT  INDEX 


323 


Electrolytic  conduction,  119 

dissociation  hypothesis,  117,  133 

solution  tension,  307 
Electro-motive  force,  307 
Electro-negative  colloids,  189 
Electro-positive  colloids,  189 
Emulsion  colloids,  201,  210 
Enzymes  as  catalysts,  291,  294 
Equilibrium,  chemical,  247 

constant,  247 
Equivalent  conductivity^  126 

relative  lowering  of  solubility,  30 
Exchange  of  ions  across  a  membrane, 
160 

FEHLING'S  solution,  174 
Fermentation  of  glucose,  299 
Filtration  of  colloidal  solutions,  198 
Freezing  point  and  molecular  weight, 

106 

and  osmotic  pressure,  104 
of  blood.  Ill  V 

GAS  electrodes,  314 
Gaseous  diffusion,  13,  16 

osmosis,  24,  78 
Gas  equation,  10 
Gases,  absorption  of,  20 
Gases,  kinetic  theory  of,  6 
Gas  laws,  1 

Gastric  juice,  acidity  of,  820 
Gelatin  filter,  199 
Gelatin  solutions,  osmotic  pressure  of, 

183 

Germi2idal  effect  of  electrolytes,  163 
Gold  number,  214 
Grades  of  colloidal  solution,  196 
Gram-molecule,  10 

H^EMATOCRIT,  71 

Haemoglobin,  osmotic  activity  of,  182 
Heat  coagulation  of  protein,  239 
Henry's  law,  20,  223 
Ilydration  of  dissolved  substances,  28, 
32,  53,  134 

of  ions,  135,  155 
Hydrogen  electrode,  314 

ion,  153,  165,  166,  280,  285 
Hydrolysis  of  esters,  168,  279 
Hydrolytic  dissociation,  260,  318 
Hydroxyl  ion,  153,  166,  168,  285 
Hypertonic  solutions,  59,  73 
Hypothesis,  Avogadro's,  7,  114 

of  electrolytic  dissociation,  117,  133 
Hypotonic  solutions,  59 
Hysteresis   in  colloidal  solutions,    184, 
186 

IMMUNOCHEMISTRY,  270 

Incomplete  reactions,  244 

Inorganic  catalysts,  286 

Intermediate   compounds   in   catalysis, 

301 

Inversion  of  sucrose,  277,  294.  295 
Ionic  conductivity,  143,  150 

dissociation,  117 

mobility,  145 

reactions,  141,  257 


lonisation  of  water,  316 

Ions.  117 

Ions  and  colloids,  203 

migration  of,  144,  152 
specific  action  of.  162 

Isotonic  coefficients,  60.  132 
solutions,  56 

KINETIC  theory  of  gases,  6 
LAKINO  of  blood  corpuscles,  68 


,  250 

Gay-Lussac's,  3 

Henry's,  20,  223 

of   independent   migration   of  the 
ions,  144 

of  mass  action,  246 

of  volumes,  5 
Laws  of  gases,  1 

Leaf  as  diffusion  apparatus.  16,  18 
Lipoid  theory,  82 
Lowering  of  gas  solubility,  26,  31 
Lungs,  gas  exchange  in.  25 

MASS  action,  246 

in  immunochemistry,  270 
Mechanism  of  catalysis,  300 
Mercury  salts,  germicidal  effect  of,  1C4 
Migration  of  ions,  144 
Molecular  depression  of  freezing  point. 
107 

elevation  of  boiling  point,  97 

weight  of  colloids,  187 

weight  of  dissolved  substances,  45, 
90,  95,  106 

weight  of  gasej  and  vapours,  10 
Molscules  and  atoms,  7,  8 

NEUTRALISATION  as  ionic  reaction,  259 

Neutral  salt  action,  257 

Normal  temperature  and  pressure,  9 

OPTIMUM  temperature,  304 
Osmometers  for  colloids,  181,  183,  185 
Osmosis,  gaseous,  24,  78 
Osmotic  pressure,  33 

and  boiling  point,  93 

and  concentratiop,  41,  47,  52 

and  freezingrp~oJnt,  104 

and  gas  pressure,  44,  49 

and  temperatur«||il,  48 

and  vaBiavaJfcpe^sure,  87 

in  plant  oens,  62,  65 

of  blood,  70,  72,  181 

of  colloids,  180 

of  dextrose  solutions,  48,  51 

of  sucrose  solutions,  41,  49,  51,  53 
Oxygen  electrode.  315 

solubility  in  water,  22 

PARTHENOGENESIS,  artificial,  73,  165 
Partition  coefficient,  222 
Permeability  and  surface  tension.  85a 
of  membranes,  63,  64,  67,  75.  159 
Physiological  fluids,  conductivity  of.  136 
Physiological  salt  solution,  72 


324 


PHYSICAL  CHEMISTRY 


Plants,  gas  exchange  of,  16,  24 

Plasmolysis,  58,  80 

Potential  differences  in  tissues,  158.  159 

Precipitation  of  colloids.  201,  208,  210 

Protective  action  of  colloids,  213 

Protein  and  electrolytes,  212 

Protein  as  amphoteric  electrolyte,  264 

degradation.  138 
Proteins  and  adsorption,  238 
Pure  water,  170 

HE  ACTIONS  between  ions,  141,  257 

reversible,  244 
Reaction  velocity,  276 

temperature  coefficient  of.  302 
Resistance  and  conductivity,  125 

cell,  124 

SALT  solutions,  114 

additive  properties  of,  139 

colour  of,  142 

solubility  of  gases  in.  26 
Saponiflcation  of  esters,  169,  283 
Semi-permeable  membranes,  34,  37,  75 
silver  iodide,  solubility  of.  313 
Size  of  colloidal  particles,  194.  200 
Solubility  of  gases,  20,  26 
Solubility  product,  267 
Specific  action  of  ions,  162 
Specific  conductivity,  125 
Static  diffusion,  16 


Strength  of  acids,  252,  255 
Sucrose,  inversion  of,  167,  277,  294 

osmotic  activity  of,  41,  49,  51,  b» 
Surface  energy  of  colloids,  219 
Surface  tension  and  permeability,  85o 

tension  in  vital  phenomena;  234 
Suspension  colloids,  201 
Suspensions  and  colloidal  solutions,  192 

TEMPERATURE    coefficient    of    reaction 

-'  velocity,  302 
Thermometer,  Beckmann's,  101 
Toxin-antitoxin  reaction,  215,  270,  274 
transport  number,  148,  149 
Tyndall  phenomenon,  192 


ULTRAMICROSCOPE,  193 
Unimolecular  reactions,  279 
Urine,  acidity  of,  320 
freezing  point  of,  112 

VAPOUR  pressure  of  solutions,  86,  87,  90 
Velocity  of  ionic  migration,  152 

of  reaction,  276 
Volume-normal  solutions,  48 

WATER,  conductivity  of,  170 

dissociation  of,  170,  259,  316 
Weight -normal  solutions,  48 


AUTHOR  INDEX 


ABEGG,  305 

Amagat.  2 

Appleyard,  231,  235 

Armstrong,  281.  292,  295,  297,  298,  299 

Arrhenius,  116.  242,  255.  257,  270,  271, 

274,  284 
Avogadro,  7,  43 

BARGER,  92 

Bassett,  175 

Bayliss,  138,  187.  237,  291.  301 

Bechhold.  213,  216.  217 

Beckmann.  98.  101.  108 

Berkeley,  Lord.  50.  90 

Eerneck,  290.  293.  303 

Billitzer,  219 

Biltz.  95,  187.  208.  209.  216.  234 

Blackman,  16 

Bodlander,  202 

Bogdan,  111 

Bohr.  25,  26 

Bouchard,  112 

Bousfield.  135 

Boyle.  2 

Bredig,  190,  219,  287.  290.  293.  303 

Brode.  286.  290,  301 

Brown.  A.  J.,  37,  294 

Brown.  C..  78 

Brown.  H.  T.,  16.  295 

Brown,  E,.,  197 

Brunner,  302 

Bruyn,  Lobry  de.  195 

Bugarszky.  265,  318 

Bunsen,  15 

Burton,  190,  191.  194 


.  281.  283.  297 
Callendar.  32.  53 
Craw.  199.  242.  272.  273 
•Czapek,  83.  85a 

DAKIN,  113 
Daimeel,  167 
Danysz,  215,  273 
Davis.  233 
Dempwolff,  167 
Devaux,  24 
Donnan,  159.  175,  187 
Drabble,  65 
Duclaux,  181 

JElSENBERG,  216.  241 

.Emmerling.  292 


Ernst,  287,  305 
Escombe,  16 
Exner,  23 

FARADAY,  145 

Findlay.  46 

Fischer.  A..  64 

Fischer.  E..  299 

Flusin.  77 

Frazer,  46 

Freundlich.  202,  206,  227.  230.  236 

Fiihner,  85b 

GAY-LUSSAC,  3,  5 
Geffcken,  29 
Getman.  32 
Glendinning.  295 
Goebel.  25 
Graham.  15.  177 
Guye.  Ill 

HAMBURGER,  69,  160, 161 

Harden.  299 

Hardy.  191.  202.  204,  205,  212,  219.  264 

Hartley.  E..  50.  90 

Hartley.  H..  171 

Hasselbalch,  319 

Hedin.  71 

Henri.  194,  294 

Henry.  20.  42.  223 

Herzog.  305 

Hill.  C.,  292 

Hill.  T.  G..  66 

Hittprf.  148.  173 

Hober,  164.  218.  319 

Hoff,  van't,  42,  44.  132 

JAKOWKIN,  222 
Jones,  32 

KAHLENBERG,  141.  176 

Kastle,  292 

Koelichen.  170 

Kohlrausch,  143,  144.  151.  172 

Koppe,  160 

Kronig.  163.  175 

LANDSBERGER.  102 
Larmor,  44 
Lessing.  1»» 
Liebermann,  286.  318 
Lillie.  185 
Limbeck.  160 


325 


326 


PHYSICAL  CHEMISTRY 


Linder.  188,  193,  196,  206 
Loeb.  73.  165,  207 
Lpevenhart,  292 
Lowenherz,  316 
Losev.  236 
Lowry.  135 
Lucas,  306 
Lumsden,  102 
Lunde"n,  263 

MACALLTJM,  234 

McBain,  233 

Madsen,  271 

Maltby,  143 

Martin.  199 

Masson,  174 

Matthaei,  305 

Mayenburg,  67 

Mayer.  207 

Meyer.  11 

Michaelis.  209,  219,  237.  270,  319 

Molisch,  23 

Moore.  84.  182,  280 

Morley.  5 

Morse,  46 

Mylius,  209 

NERNST,  153,  224,  273,  302,  311,  317 
Neubauer,  856 
Noyes.  268.  269 

OBER,  206 

Osterhout,  68,  83,  207 

Ostwald,  W.,  142,  167,  198,  250,  252 

Ostwald,  Wo.,  220 

O'Sullivan,  291.  301 

Overton.  79.  85.  162,  165 

PAAL,  213 

Pantanelli,  65 

Paul,  163,  175,  264 

Pauli.  210.  211,  212,  239.  2C4 

Perrin,  198 

Pfeffer,  38 

Philip,  32,  269 

Picton,  188,  193,  196,  206 

Planck,  311,  317 

Prideaux,  321 


RAMSAY,  78,  198 
Ramsden,  234 
Raoult.  76.  110 
Rayleigh,  2 
Regnault.  10 
Reicher,  132 
Reid.  180.  182 
Ritzel,  31 
Roaf,  84,  182 
Robertson.  83,  211,  319 
Rona,  209,  319 
Rothmund.  32 
Rutland,  83 

SCHAEFFER,  207 

Schryver.  139.  264 
Scott.  5 

Senter,  164,  257,  291,  304 
Siedentopf.  193 
Sorensen,  320 
Starling,  181,  301 
Steinbrinck,  23 
Svedberg,  198 

TAMMANN,  36,  56,  76,  297,  30-i 

Terroine,  207 

Tijmstra.  167 

Tompson,  291,  301 

Traube,  75,  85b 

Travers,  226 

True,  176 

Turbaba,  289 

Turner,  103 

Tyndall.  192 

VEQESACK,  187 

Veley,  305 

Volk,  216,  241 

Voss,  213 

Vries,  de,  58,  60,  61,  62 

WALKER,  89.  102,  231,  235 
Waller.  305 
»Veimarn,  201 
Whitney.  206 
Wiesner,  23 

YOUNG,  299 
ZSIGMOXDY,  93,  197,  214 


Printed  by  BALLANTYNE,  IlAXSON  &>  Co. 
Edinburgh  <SJ  London 


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